{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IDFT\n",
    "IDFT(Inverse Discrete Fourier Transform), 傅里叶逆变换，可以将频域信号转换到时域中, 它的公式非常简单：\n",
    "$$\n",
    "x[n] = \\frac{1}{N} \\sum_{k=0}^{N-1} X[k] e^{j2\\pi kn/N}\n",
    "$$\n",
    "\n",
    "$X[k]$：离散频率下标为k时的频率大小\n",
    "\n",
    "$x[n]$: 离散时域信号序列\n",
    "\n",
    "$N$: 信号序列的长度，也就是采样的个数\n",
    "\n",
    "对比我们之前讲过的DFT，两者公式类似，但是注意在DFT中指数带**负号**，而IDFT中不带"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 从矩阵的角度看IDFT\n",
    "\n",
    "## DFT的矩阵表示\n",
    "讲IDFT之前，我们先复习DFT的矩阵表示形式：\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "s_0^0 & s_0^1 & \\cdots & s_0^{N-1} \\\\\n",
    "\\vdots & \\vdots  & \\vdots &  \\vdots\\\\\n",
    "s_k^0 & s_k^1 & \\cdots & s_k^{N-1} \\\\\n",
    "\\vdots & \\vdots  & \\ddots &  \\vdots\\\\\n",
    "s_{N-1}^0 & s_{N-1}^1 & \\cdots & s_{N-1}^{N-1} \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "x[0] \\\\\n",
    "x[1] \\\\\n",
    "\\vdots\\\\\n",
    "x[n] \\\\\n",
    "\\vdots \\\\\n",
    "x[N-1]\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "X[0] \\\\\n",
    "X[1] \\\\\n",
    "\\vdots\\\\\n",
    "X[k] \\\\\n",
    "\\vdots \\\\\n",
    "X[N-1]\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "$S$矩阵中的每一行都是一个$S_k$向量，$S_k = e^{-j2\\pi kn/N}, n=0,1,\\cdots,N-1$，进一步简化上面的表示，得到：\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\cdots & S_0 & \\cdots \\\\\n",
    "       & \\vdots &     \\\\\n",
    "\\cdots & S_k & \\cdots \\\\\n",
    "       & \\vdots &     \\\\\n",
    "\\cdots & S_{N-1} & \\cdots \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "x[0] \\\\\n",
    "x[1] \\\\\n",
    "\\vdots\\\\\n",
    "x[n] \\\\\n",
    "\\vdots \\\\\n",
    "x[N-1]\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "X[0] \\\\\n",
    "X[1] \\\\\n",
    "\\vdots\\\\\n",
    "X[k] \\\\\n",
    "\\vdots \\\\\n",
    "X[N-1]\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "## IDFT的矩阵表示\n",
    "从IDFT的公式，可以看出，其实IDFT和DFT表示是一样的，只是对象发生了变化。具体来说，有两个变化：\n",
    "  + 由于指数部分不再有符号，$S_k$进行了共轭操作，得到$S_k^*$\n",
    "  + 输入是频率信息X[k]\n",
    "    \n",
    "因此，矩阵表示变成了下面这样：\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "\\cdots & S_0^* & \\cdots \\\\\n",
    "       & \\vdots &     \\\\\n",
    "\\cdots & S_k^* & \\cdots \\\\\n",
    "       & \\vdots &     \\\\\n",
    "\\cdots & S_{N-1}^* & \\cdots \\\\\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "X[0] \\\\\n",
    "X[1] \\\\\n",
    "\\vdots\\\\\n",
    "X[n] \\\\\n",
    "\\vdots \\\\\n",
    "X[N-1]\n",
    "\\end{bmatrix} = \\begin{bmatrix}\n",
    "x[0] \\\\\n",
    "x[1] \\\\\n",
    "\\vdots\\\\\n",
    "x[k] \\\\\n",
    "\\vdots \\\\\n",
    "x[N-1]\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Talk is cheap, show me the code\n",
    "\n",
    "接下来就简单多了，我们将先介绍如何使用scipy中ifft，然后自己动手实现一份ifft"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "导入必要的包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.fftpack import fft, ifft\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成信号用于测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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78FYcbTSbrb1oHAg2Gkf0SJSXwb3RbE7FTIDxwuM2lJvt2Rn/jZaHxUoBpcJ4WR1cKKPbH6Ht8WarbLf3G+SDC268jJ22h+WpjcYFndXtD9Htj/ZsnvkcYanCv463gzm9XB3rWgrGuMuuK6Aea/u96m2HrbHT5NY2/tUieoORgyCit2eCAv7D5H6Q3f4Qnf5wD1/tSlfIjU9saoV8DkuVojskFEH7cHsZm839C88Z8m/v36hD954Zke90vH3I31UsI8rLWK4WsdvlnYNbEUYSAJaqBWfGf3K+yw3Ola7J+MwBRzEuHbmljb+rnXyn3d/zIAH/wXI/SPm9p1HXgRr/Ipd51EszQHg7wX1anlp4RMAm86a21fbRuCzkAdwZ/82Wt89wyXniwqBMz8GlShHekBfsjEbCp30ijD/3mCTlNz0uF7q2O/sTAcqFPCrFnDvjP3EP5c/cXrWO3NLG38VO3h+O0OgNsFKdXuQl9AYj1lbB253oxbBSK7FzhRLFLVWmNxp+L2O3O9inq5D3Wz1sMtM+O539RlLOCxfI9cC0QXZFJUQY5CUH42p6A4zE/jm4VCmwF17JOR31vOSc4ZKtCIMsdbnYaBbLhbB4Epjg/G/2gC8RPUhEzxHReSL6UMw1/5iIniGip4noP3PoTRMXxn83xiBLxCcRBYfsxCJ//oBvvC4XXkYf5UIOlWJ+z/vL1SK7Qdnt9PdtaItBwRy7RxhlkCv8BlkIgZ12f4/nBExsaozj2mlHzwtJ+3CefCXBzrT35MIgR3mf7nTtf1alQg71Uv7mRv5ElAfwUQDvAnAvgPcR0b1T19wN4GcAfI8Q4vUA/hdbvSriwvjHoXGJ+DizVcbu4hTnXy+h0+dNVZQGY5r2WXLA7e52+/v0AL5RbrjQNWX8pXvPjSYb3UHE/ZMbDZ+uTn8IbzjaNy9kFfgOo67tGOO/VC1CCN8z4JJYzt9BwHervT9VFnCF/Pd7n4AbD15HOJD/WwCcF0K8KITwAHwMwENT1/wTAB8VQmwBgBDiOoPeVHFi/OOQUBi953uYcW6wXOQNRuO12x2ACFgMCtcmdXHqAXxDKMewVxe/e7/bGYQGeJ8uxnkhhECjOwi9ilCPAyomKoDoStdOCHamg7DB2mJErnHjcmKQ2/19m8xYFz+dNb1RA/44t5nHpSMcxv8EgAsTry8G703KPQDuIaLPEdEXiOhBBr2p4sb4x6MTAKzGK6RiatO0hf+aEyXvdvpYKBfCniqTuhrdPmtXxVki/0a3H96v/br4nlXbG2I4Evu8jIVSAUS8VExUABGYmIOsnm5Aj8yAztrt9lHME8qFvWZpqVqEx5y1t9PxIufgUpUXFADRwXnAzXzXEQ7jTxHvTVuKAoC7AbwdwPsA/DoRrez7IKKHiegcEZ1bX1+3/mJjN5gfCU1PHIn4OFstb7f7yOdoHxoPOWtW5L+fHpG6RgJoMQayo3h4QKJxZuTfHUTrYqaz5EYyvdHkguc3C1AwpphcIP/o+ALn2mp2B1isFMM+VtO6OMe1G+GlSV3snH8nDuwU2b1qHeEw/hcBnJp4fRLA5YhrPiGE6AshXgLwHPzNYI8IIR4RQpwVQpxdW1uz/mKFvB9UYZ2gPbnIpw2yAzTe7WOxUti3GFwh/2l050xXBDcudXHqGY4Emr3Z0D5htlSULmY0uROg8f2cP7/3Gc/588cyomgzX5ebjSaOemz2Bhgwnrvc6EWPi9v71BUO4/8lAHcT0e1EVALwXgCPTV3zRwC+DwCI6BB8GuhFBt2pwr2TjxFeNBrnfJhxi8GFrlhuvOpiXP2YRV5AyxuyLbxmRErpWBdvfEFuWtEUE6+uOG68UsyjXMjxbmoxmVkuKKa4eeHCy2j0ounAcRowz/PqDYbwBqNYT/empn2EEAMAHwTwSQDPAvi4EOJpIvoIEb07uOyTADaI6BkAfwHgp4UQG7a6VYQbdTW6A5TyuX1ZAsV8DpVijvVhNroDLJSjqRj/97zINZr24UX+Qogg4Buvi4s6G6Nx93xrWCQXiSYLvAHfmLRcgJ/OiuOrJeXETZ0tRsx3F3UZ/tpyv9FIABKla7FSQLM3cHJKmYrs/0YGIoR4HMDjU+99eOJnAeAng38zFX7kH41OAH4Or9mLQ8jSIHMi//ggrP97LiQ0gjccxVAxYy9jOrvERORzj7yHQXxBCLGPVjOR3QTkv1Qt4sIm38Hg220/MFor5ff9jrv4arsTnaniIpDd6A5w28Havve5DbIQIogvuDf+cUyBfE/G06I2B9dyS1f4AvzGv9kbYCHW+PNyeD4S2q8rXHjMqZ7RrqkMLvPcw7CeIAH5cz2vuKplwKeYvOEIvQEPxRRWLcfEFzjnxU7Hw3K1FLlpLTHP96jCNcAPZHPn38dlZoWJG0xppd3+CIORiKZ9mNtxSC82Gvnzx9N0JDP+mhLHwwOS2+XdaKJ05XKEhRIfbTEYjhIDowCfl5FExXDHFxopBnny+9jrSt5ouDNVouglqZ+b9pnOKgp1VXmzmNICvly6xvEZ98g/ySN0EbvTkcz4a0qj24910ZYCDo9P12y8DPk5Sdk+XAZlJ5Eb59WV5GWMe+4wbWodGQvav6SWKkU0egO2s2HbvUF4ity0LDuIccWBHc61NRoJNL3oTa3InLW3m0DFzJb2yZC/U1muFtHtj9Ab8OSpN4Jc5Cjhpn2aMQFfXxdfpkASPVIp5lDI0WyQP7uXEZ/ts8hMZ8lYUBwVA4yDf7bS8oaRfL+vixeNt70B6qUEL4PJSLa8AYSIRsgA70YTl64t9QB8sYxmCucP8NK3OnLLG39uhBfHwwM+r8dlkHsDv39LPMXEt9HEtXMGACLCUpVxo0lE47xFSvJzorwn7lTFuNoFXxfvRtP24pG/NMhcGSRtb4haOXqj4TTIci7HebqcsYyktNxKMY9SPsdOB0Zy/uWM9nEq8qa3mOiYOB4e4M32SXIX5ft8VIw0yAm6uOiRBB5+gXkxyI06n9uPxpfZ4wvxWWDcRUrt3hDVWORfxGAk0GaoyB4EAfFE5M9mJJPnO2dOfLjRxIG4SoHVXsjPnJaM9nEsEiFxcPFCiNRsnzZTkVKSu+i/z7fRJFEx8jvMAvnLimw2zj+mh9Ckfs74QtSYXOhqeQPU44w/o6520EsnkWJi86jj0TgA1Mt5tHpc1G18wFfq4qLoGt0BSoX9dUGT+jPk70g4kX+n7zfviuf8+YqUxili8ZkWnKgVSNhoyrwbTSmiYjTUxRnL6CTXZPjXMHoZscift1ai7Q1Ri0PjjLragbGNo5jq5UK4JmwlDfnXy3zJFHF9mEJdpQKaXBtNLz4zq1bKI58jto1GV255418P+MoWQ9/xNHeRcyffTeAKfV183TYloorNYqryUUxx7Zz36GKjmOLReKWYQzFPvF5GGvJnoH2E8CmdegwPz+npyjUTh/xDYMWwtsZJB/Fri9v4x9I+ZT7aJ66SGPDjaZxxQl255Y3/uNum/U6ezkvyGf902qeA/lCwFCm1w0XunmJKClaGunp83G7c/SMi1myVJF2cRrI3GGE4ErHPitPTDZF/jK46o65xBk48Guc0yPUAdUfJQqXA8qwAoBlTuCbltWzudssb/xAJMdzgVHqEMYCTHvDl43Zb3hDFPKEUkaMuvwPXBG31hqjGUD4Ab3uCVkI+PODPDQ6DMhiO0PaGsYtcZsuwGGRPGuQY5F/iM8hpyJ/T+KvQPm1vyHJsZDOmqdukLk4vI6l1A3fTPx2ZG+M/C3TCSfsklYUDvF5Gx0szyH6bWw5ut9OfjUEGkEiPhLoYsmLkZ8QlApQLeRTzxOJ9yntTS6AsJr+TjYQeYawu/97yeNX+2RVx85DTe0oqngT89ilcPHxSdiDw2h7ocusb/xIfB6qKxjloi6QUscnvwGH80xCy1MWx8Fq9+AIlwF/kXKgrKTAK+OiZB40nI2SAb1MbI//4TBXg5vMyJG0W12RvDOJ46Nskg8wJQJKKQgE3x6Sqyi1v/PM5v/shzwRNC8LyBnzjUsR8XXwUUzuhYhQYxwLaDAsvqWJU6uLIURdCoOUNZmqQE3WVeHjkkIqZQcBXPu845M+pK90gSy+DZx0nGWSf8+ehmOSBTHHCGePSlVve+AN8HF5aihhnkVLcSUNSpKHhMJS+kZzNwktH/vmg1N9u4fUGIwgRH8T2dfHQPmmBUUDmqbsPwpYLOeRzxMr5xyF/zuBy3NkVTnSlUDGSzmpbnhks64KSdfFRTLoyF8afi0pISxErF/w+OG0GhNfsJQeKOF3uNOQvdXGMq9OPbxcA+Bu1EP51NiLvSxLnz+URpgVG/e9RYKEs0nQRESOdJT0a99k+bW8QGl3XupoJLVo4dbW8IYSItxdSF+f52DrCYvyJ6EEieo6IzhPRhxKu+0dEJIjoLIdeVeFCXc3eICzMiBIiSTHx8JJJQak6c2AvifOvsSL/FNqHiUqQhispkM3lEXa8ZHoE4AMgKvEFXxdPcDkpC2whfFY8QfM0Lw3wUbutpMWCuDz48BSvpHVcysMbjNBnPDNYVayNPxHlAXwUwLsA3AvgfUR0b8R1iwD+OYAv2urUFT9H2L2RBPh45GZKihhrYE8hCCuvs5HhyK9LiOtL4+vKs+gKg5Up97DtDa0ppjR6xP8dc8A3BU1yeGntlCywSjGHHHHNwUFqZhZgr0vGghJ1MXnVcl4kreMa09oyEQ7k/xYA54UQLwohPAAfA/BQxHU/B+AXAXQZdGoJV3VgqzdMXODAOB/ZVtJon2oxDyJ/0diKasDXNmDZDo1kcsAXsEf+qlSM3JBsRC7cpE2Na16EQdgUXWxeWsIcJCI2XamZWUxgp9tXiAVVeIz/+Fmlxxe4isp0hMP4nwBwYeL1xeC9UIjoTQBOCSH+hEGftvBN0OTAKBCkD3Jx4wm6fG6XK089eVzjYBsPGk/i/LkCe2oLj4tiSt/U6uU8c8uFlEA2x3zvJ4MCTl1pmVlcFFPopSnMQS4AkgQYa4zxNF3hMP5RBHjoRxNRDsCvAPip1A8iepiIzhHRufX1dYav5gsXFdPqJRcNAf7D5NGVvBh8XfaxjLReMQBfhWpYoJSCWgH7LCYVbrzG5t6nb2pyDtpSTG1viEoxFxt38nXxxJ2STgwb6+JJYfWpx2RPl4NiUgEF43gaDyhIigXVGQvldIXD+F8EcGri9UkAlydeLwK4D8BfEtHLAN4K4LGooK8Q4hEhxFkhxNm1tTWGr+YLZ7AtFfkzZXV0UtxggCdVMa1XDDDBgVovBoWFV+IJLqtw46HLbfm8Ot4Q+RyhlI9fTgvlAgYMFFNawBxgpH1S6MCxLrv75w1G8IajRITMRTEpxWeYDHIrTMtVyKRjPP5VVTiM/5cA3E1EtxNRCcB7ATwmfymE2BFCHBJCnBFCnAHwBQDvFkKcY9CtJAvlAnoMEfU0bhyQQUSeoFQq8mfIYgozVRJ05XOESjHHgMZV8uF53GBVzn/yWhtdtVI+tjoVGBsAa+SacLLWWBcTGk8pyAOCugyuOZjiZXBQTCpofLHMc+ymHFdaLAjgydrTFWvjL4QYAPgggE8CeBbAx4UQTxPRR4jo3bafzyFcmQJpQSnAR7W2iKE3GGEkkmkEqYsrIyF9kfOhrsTFUOLhdlU2Na7gcrs3VELjgD2dpYr82bLA0mgf1jmY7mVYb9QKaJwri0llbdWYQIGJJD9ZRRFCPA7g8an3Phxz7ds5dOrIwkSe+kqtZPw5aSligD+pbFFrSI8kpNkBvkFeb/R4dClsNLauaSekYtJdbltdLY2Ar3VaqUJglKsVgor3uVDOoz8U8Aaj2Bx9FUk6MWysyx4UtBWRPwfFlNa+HOCjmFTWFpf3aSJzUeHL1RQqLSglddm2nlVxTQGegK9KXxqAZ+GFVbcJ97CQz6FcyKHJEGyTrQ7ihCt9sN0bpFMxbFWjakFYDl1JZwVL4aAe24rIf6GcR9Oyl1WI/FOeFwfF1OoNUEiJBdWZAIiJzIXx50jdUglKARPI1aI9gbJBZuB2JcJWSWFl82hU3HuGTS3VSDLWFNSK6dw4h652ynkIAI+XERZDzSDBQcVLA3iKNcfnEqskU/B4aUmxIPksuTrZ6khm/BVFNSg42a6CAAAgAElEQVRVY4jeqwRGAaaFp6XLfbaPrytvjYRUAuZcweWOShCWK4U15TwEgKf3vWrcaaFUgDccwbPIYgqRvwIat9881XTVy/atltOK5ACEZxjcrHn+3/IijU3H4ga3+6pBKVmxZ4H8e+mBUanLtgPmmGJS0WXPtxL5AbVEXSWORZ7OjZcKOZTyOYbCIYWAL2NwWXVTs9msdQCIra6WMihgCPh6Q38OxrRKH+vKh4DPVFTiM1LXTZntczPIOKJufoPl36YaZIbCIdWFVyv5HTC7fRvUpUExMQRh66X4AztCXQytENopFdJSWDjr3kBho54d589xwpZKQZ6vy35T00Hj1sH53sAvGEuIBQFAtWhfQ5NWOS+F8/AYHZkr42/Hw6ulRPIgITXkz8Ejt1Q5f6Yc67Qx+d/FvhVCW6FCGmCKm/RVej7ZB5eHI4Fuf6ROZ3EAENXgssU9VEX+tVIe3tCuXiete+ikLhumAFBH/jWmxpO6Mh/Gv2xP+4RBqdSUSPtDVlRSIn1d9py1ehDWvgNm20s3kgBTpoXiImcpHFLIh+c4x1cZgDBQTCpFcsB4PdjM97ail8GxttoK6drAeL7biEoXYIAnmcJE5sL4y4i6ze6quvA43OAQCaVkkHBkdbS9IUr5HIoJ6WiAv9HYtidQaY8B8NA+HcVFXrPsg9Mf+llgaTUZgL33pFqTwRFcVumBA0y2J7CgmLwhSgW1OQjAiotvKaRrAz7tY238FeIzQEb7OJV8jlAu5KxOh2qponGGDJKOIu1T50BdXnqOOjBREGW98FSoGHvaR6UvDWCf0qdaoAT4htLu/qkBkDDGZUXF6KFxu3uYXkw2qcvO01XX1bZMplBJlQWygK9zsT3gouMpcuMcwWVvmHiCkhSOrpQyCJsmHGXo7X46PQLYPytAcv5q47JD42pZYFLXLCg6Wdxmg8bH6ZeqbSvs5qASGmegfVqe2hyslfMYCdh5ur30FGCAp3reRObG+FeLdrnj454ginn+VhuNOl89+d2MdPXVAqMcuePtnhrqqpcL6A8FegOzcQkhlIKwgD0aD4+LVDb+DMg/xXiFx4kybDSpgWwGsKPKw7Nw/opzUNJ4prpUi+QABGeAZMjfmdguvLYiFcORO67Syx9gcu8VqZgaQxZT20tvFwCMx2XK7crTmqqKqZ4c3Lia92Tn0agif3mNDTcecv5pRY0cyF85A4cnwWEWulSL5AC+sx50ZX6Mf7lgleqpSsX4uizde4VGYQBXMY8aPcLR+16lRTAweX6AmS6V05qk2HZGDblxxQwSOzpQjXoEZAqrva60VhIsyRQp5/dKmWW2j3yephuoanNGwF/Hg5GAN+ND3OfH+BfzdnnPihwyYN+DRJX24VgMKqeTAX72g7UuhTYIwET6oOHzGrdzVruH8kAb17qqpYJV0oEW8i9bzvfg8PakxnjA+KwH22SKmc13TV3GAESmr6rEF+S4ZpzrPz/G35ZvVcxRByTCsyu8UlngYWDPJr7QHyrRI+PMIjNdg6D/i1Zw2RL5qxZ5AebjUu1FL6+x8tIUOX8g8Gis6EC1OQjYV3+rZ+DY1ev0wzmoA3bMdKlW6QN87b51ZX6Mf9kOdXUUswQAH+HZUEwdRdqHiFArWlIJqgEwSypm3E1RXZexQe6p67LNIJFoTSWWUWUAIIDqpmYb41Lz0gD7uElLoUgOsEf+Wmm5lrSPDh0YxrgsbIaJsBh/InqQiJ4jovNE9KGI3/8kET1DRE8R0RNEdBuHXh3xjaQdt6uM/Et2LnerN1DeaGqWDajUA2ByMRgiIcWiIcC+cGhcIa3j0ZgaFLXce3mNTe542xuENStpUrMsHFI5MUzKrJB/GF+wflY6yRR2oEArxnWzIX8iygP4KIB3AbgXwPuI6N6py54EcFYI8R0A/gDAL9rq1ZUqQ/aDKudvSzF1vKFSoMjXZe7eCyGUA2C2gT2dIGw1XHh2VExasBKwr5UI0bhiLMMmd1xmZqU1xgOYkL8i2LGZ76ORUAYguaD9sSkAaSlmMAHjTDFjXRrUY7Vk52WYCgfyfwuA80KIF4UQHoCPAXho8gIhxF8IIdrByy8AOMmgV0vq5TzaffPeNCpHOEqxTelrKRxEMtZlvqnJdDQVyiKXI6sipZAeUcp+sM200OHG7VxuicaTTmsKdVnmjqtmSwH2WUyqfWkAu1bL8r6rry3zjSZsX64yBy3rF3TmoG12m6lwGP8TAC5MvL4YvBcnHwDw/0b9gogeJqJzRHRufX2d4auNpVYqYGjRm8bPUZ8d8lcxyFKXMUJWbBewV9csDLJlfEGxQGmPLkNDqXJaU6jLMjVXNVsK4Khr0UT+lh6hqldtEzdRbc4o9QA2oMAk7nST0T4AomZ9JLwmoh8FcBbAL0X9XgjxiBDirBDi7NraGsNXG4tEnMYBHMXAKCCRv5ke2ShMR5d1LvK3mK5x6pull6FUK2Ef8NXhxu10afDwMnfclGLS9DLkYUe6EnLjipta3cKr1onPlPJ2mXRtjaQDjh5dJsJh/C8CODXx+iSAy9MXEdE7APwsgHcLIXoMerXE9mxd1dx7wK4p1LhdwCzQuHoQNtRljFrVEV4x71dJmz4rHV01y/oFleMiQ12WCE+1WR2HLtW+NFLXzYD8x2cUKGbSlcwz6WY5B02Fw/h/CcDdRHQ7EZUAvBfAY5MXENGbAPwafMN/nUGntkhjaoImwz4dGqlvpoE9nYwEwA6N66SjAXatlrW9DIsipY43RKWYSy1Qknr872euS8dI+rrMqTOd3HvArlZCuajRgvPXyYcHmDh/DV02nq7qHKxaerqmYm38hRADAB8E8EkAzwL4uBDiaSL6CBG9O7jslwAsAPh9IvoKET0W83HOxCbYFvbpUJ00Frp0GoUBdpy/Tjqa1GWOJNU5fyBIzZ2F4Qo5f/e6WOILGinAgJlBUT0xLNRVyqPbN6uSHlfCuo9lqDZnHOsyr9fRSZX1zzIgq9ogE1H7dikihHgcwONT73144ud3cOixEZsTh8bdFFVR63iRr9ZLWrq0DbJFgc0YCakvvPWGGWOnU6AEBEV5Fjy8qp5KMQci85S+jjfEAcVnHPaLMQ0i9jSqzC2Qvw43Pnld2xtgsVLU1KVvkI1rTRSbM451mXufOkVyvq7Zt3Wenwpfi6pRE24cMFvk2ga5WIA3GGFg0BRKl4qxOe+24w2RIygVKPm6LDwaTz0IG1ZJG3sZ+gHf2XgZ5sg/7FekQXMCdsBKB4DYPKtSPqfUnFHqMvcy1JG/rS5TmSPjbzFBNXl4m4o9nRJ0wC6QPS680gi2WRiueqmglBLJoUsV3QH+vbahs1R12aT0+QV5ak34gMmD1U3mhR4aZ5nvGvfQ3CNUO7VurMuc9lFt0SIlM/4OxaZHvC4Pb1OxZ7IYALNWCB1d5G8T8NXIHgGClD7T9EENIwlYBhEVD42ReuT30xXZeVQnK8bXpX8PddG4TX8kXQBi0yJDx0vzdZnTPi2NLsCAfWGoicyR8Tc/iWqci6yJhCwWg0ol7KQus0WuT2d1+kOjwJ5/RoHGYigXjJG/aruAUJdFC+62YlMyIEhhLeTM5qBG4Zp/nTnFNE6JdF+/0O7p0YHVkl0mnQ4at00r1UX+N2OF700hHLSPPhIy51t1qBhfl1l8QbaFVhGrWIZGi2BAZvuYB/b0XW59XbIgT7UPk9Rl4hHq9If3r7NA/rqBUXnQj6GumgYdaLWONRIBpC7T4HxLoz1GqCsz/m6kXMghR6ZUjGb2g00ATHOjsUFd+hPUwsvQqBgF7LKYVA8ED3UZIjzd+AxgftCPdlaMTbqxZsaZTRfWjiZCtvF0dQo1pS7jtFzdjcaiVsJU5sb4+xV7ZjdYpz88YFexp5sVY+Nl6Lqm4aZmuMh1grDyYHUTbrejifxNWwboFuQBEk2ao3HVuEkhn0PZkGLSBSA2Z0nrzkGbeJpONbbUZXrKm66uWjFD/k7FNFOgo4nwbCr2JGpVdYNtvAxtdGIRN2lpBmGrpbxRI77RSGgFYQHZtsKMRgDU6REbXWGvGA2KqW4YN9EtyJPXmcz3tjdQbmUCTG407gGIKc05LpLT8DIsz18wkbky/qY9znWDsDYVe52+LmKwo3106RHAkDrTzH6oG+rqDoYQQo+KqZXNuN2OJhUDmGd16HRFHesyi5vonLo2eZ1ZQZnuRm1Xr6P7rAD9Ta2jef+AAJjejCd53SxSNVx4HW+oFRgFzCv2tINSFoG9jnZKpF3uuC4H6v+d3rh0U2UBc25Xl4qR38sqvqBLZxl6GaonhgG28TRDNG4Idkx06T4v3UJNwAc7/aF5F1YTmSvjb7PwdBCXrS4TNG6G/DUDYBb9YnSDbcYLTzN9FTDndsd1EpoprDPIh/d1mSF/yVerUo9EZFz9bZKZ5X9H98Fl0zloMi/GJ4fNDv1nxl9BWt5AmfKx1aW7GCqFPIjM+VYTikl34XkDvTMKAPMsJt1q7L269O6hmS6zttg6/eGlGM9BTe8TCLKzDLOYdKiYccBX7x56gxEGIzGT7DbdBBFg4uSwGWb8zKHxN0WtusbflNtVLxoCxueamuc96yFJQH/hSTRj5HJrGkrdamzAvDdNaJA1npdp0oFu33t5rSmdpWOQAfO+TyZZYIA5FaMD4oyRf1+vTmLy2lm2eJgz42/mcusaZF+XWcVe2xtoZXTY6Op46qeTAeaVy7JNgwnq0tZlGBgF9HvT6JwJK0UaSd0UVp3+8GNdZkFE3Y6UgHldhmmqp77xNwvC+n9rBkB05qBN/YKpzJnxN0NdpgbZNACmvfAM2tzKlEgtiilof6yLxk3cYNNAtpEuY4pJIn+9cZm0J9DtEunrMiso0+1LA5h5GaORQKevfjY2MA4umxpk3YK8yb9VlTAFeAZeho2wGH8iepCIniOi80T0oYjfl4no94Lff5GIznDo1RXj1DcT2sewYs9IlwHyN0mJlO2PzbMf3C886XLPQlfbGyCfI5Ty6svItPLWBBTUDWlO3fTLsS7dZ6XXrwgYB5eN5+AMaR+T7LabCvkTUR7ARwG8C8C9AN5HRPdOXfYBAFtCiLsA/AqAX7DVayLVUgHd/ggjg6wObdrHsGKvbcC3mngZuo3CQl3lggEVo6+rakjFjE9rmo17r5MVA0yksGqPy2Re+EZSd763vYEBzakPdkyoGMCs3fe3Ou1zsyL/twA4L4R4UQjhAfgYgIemrnkIwKPBz38A4AHSWTFMEhYOafKgLQPax6RiT1YG6gSKAMOFZ5ASCZihyRB1GSwG3U1NtxobMK+S9k/W0t+oAf05aOIRynGZ6NIGBUYARAZGDdKoNcdkMi9M6cC2YeX35N/OQjiM/wkAFyZeXwzei7wmOPN3B8BBBt1aYtqDxMTlNqnYG7vB7pG/bv8WKVUDl9sEjY/bH5uNS4dvNT2MRLd/i42utmY1NmDejsOE8zcBO8bep0GMy2S+y0I3U69aj2K6CWkfAFEIftrPVLkGRPQwEZ0jonPr6+sMX22vmBRSyBOU9Be5fsWeDKTqI3/9WIZJAAwwQ/4mqZ6AWWquSVZM1RCNd4yC8xacv8H9A/TQpOl8lzUFOllMJmm5k7p0JNRllEmnOQf7A5QKORR0YkEWxWumwmH8LwI4NfH6JIDLcdcQUQHAMoDN6Q8SQjwihDgrhDi7trbG8NX2St1g4XlDvROUpJhsNGOuUJ+HN3W5jTh/Tdd0XAxlkDuuze2a5agD+gef6PZGAmwyi/Tab0/q0jFe3lC/GArwkf9gJOBpnCVtUgkL+JuFrpHUPSdDikl6uEmRnE2LDFPhMP5fAnA3Ed1ORCUA7wXw2NQ1jwF4f/DzPwLw58KkV6+lmARwdI86lGJSsTemLPSDy9qGy4CXlLrM0+wMeGTN9sftnl7REDCRwmoY8NUR0xRWE4NiEsswqSSevF7HyzClHuszon3k9Sa0jy4AsWmRYSrWxj/g8D8I4JMAngXwcSHE00T0ESJ6d3DZbwA4SETnAfwkgH3poLMQE9TVMjT+JsUoHRvk39fL6tA9oGasS9/lbvX0UyKBwOU2QOMmC88shVV/kdu0rTBF/nrz3dxLm/x7FTEFVia0T8cbgjTOyZjUpe1l9PUayEmxOZzeRPSecIwIIR4H8PjUex+e+LkL4Ic4dNmICd8qEYZuRoJJxZ7pRjOZQaJqIEzRuFmOtX5KJGDWIsMkOA/Ihmu6aFw/4GuSwjruD2+I/DV0mc4LE7AzTr/Up31MN2qTOajtZRh4aUAQNL/JaJ+bRmoGtI95RoL5RmOSfqmrywb5m2Sq6OoBfOM1i8AoYOZl6FZISz3AbJ6VSTsO3eMiQ10mFJNBS2xflwkoMEPjpl6GyRysFvNGDRpNZc6Mv4EbbMqNG1TsmbQmAMZeiYku7eyHYkG7/bFuL38pZmml+kFYwCKwp0nFyBRWI4RsnFmkAXZ6pty4/sEnJimRgD9nu329OWgKCoy8jL7ZHDQBOzYyX8Y/7EqpgcYN2gX41xsgob6ZG2yC/Dv9IarFPHIaKZHAJMLT43ZNqBiT9scdzSMcJ3XpjKk/1G9TLUU3hVXeA300rp/F1DKkYky9jFJeLyXS/276qbm652RIMTnf2STpADA/bMpU5sv4FyXfauIGu89+MEVdJllMrd5AO7AMmHpP5mhcu3itp9coTIpu+uA4R93MoJjMQZP0Qd0sJlMqxiSLyW8jYbZ5GumaFfI3qJAGzI+ZNZW5Mv6FfA6lfC5sMawiJqXagFnA17QQJTxAW9N4mXKggF7A0oqH12x/3NZsUy1FN33QtE4CkNXf+shfdwMN0wd1kH9Yje2+VqLtDbUpH2B8H3RraEznoH7xmhnYMdlobGSujD/gIxS9SWO28MKsDk1dJlRM1cCjMWkUBpgHLI10abY/li2CdXl4qcvESJpsoHXN4HJIBxqi5G9V5K97kEuoq6Q/302DsPVyAUPN4jVTYGVCMdnI/Bl/zYIo0/RLeeC7LjoxoWIk8tdBkx2DTJVJXbpehpEuTYopbFM9Ax4+rMmYAZ3VNkTjgH76YJh0oJ0IYEKp6tcuAJPtOPQKKI3QeFEvThgeF2ns6WbI35noutwdb4icQXGILBzSKXqxpWJ0eXibhadVuWyrS5FiMmkgJ0W3fqFliJAB/X4xptWp8m906ayyZl8aIKBUC3qUassbalOcgBkAsfYyFHWN+1iZgQJvMMJAw8uwkbkz/nXN3jQyS8CkA7UJxWRFxWiOy2jhGfCt/mlN7pG/7cLraSw8UzoQkAVl+okAJhuoSXDZRI+vS6/Pvk0+PGDgfZrEF+RGowpALDdqANrtqk1l7oy/bq8O0ywBX5eey22O/M2oGJNFrhvw9QYj9IeGbrAmj9yyCMLqLjzTLDD5N7Oo/AZkOw49L8MEFAByvutm4NjEndR0jUZBp1KjzVNvozHNzALMUtFtZO6Mv27zJFO+GjBxufV7xQDjvuOzSH3TdbmtELImwjM5NCbUpbnwwgZohnSWnpc2CJ+xrtR1AUjPLO4EBEVK2l61+RxU9Wi6AwuDrNmzyLRTqf83+pl0NjJ3xl+3/bGPxs3cYN2WAabIX+rSrVy2ck1ngITGi1xtMVjp0jxkJXTvDamzdl89fVA+KxPq0d9o3AdGARPkbzcHlTdqqzmop8uO9jFr+mcq82f8tYOwZnnjQNAyQKsK0U6X6rjClEiDRS77jqt6GVZoXLOS07Q9BqDfmMy05YLUNRwJ5RRW01gQEKSVziDjDNBvT9AxBFa6aNz0yFL/b8wCvrMAVrYyf8bfwDW1QuOaxVA2XoYqOgmPizRY5LqFQzYZOOEiV9Rl2gBt8m90KKaCQZtqX5feIm8ZtscA9LuVmlZjA/45FKqek017jHyOUCmq90dq9xnQuHbA13xTm1Wu/9wZf8n5q7rcphkJgH6zsHbPBvmrIzybCQrISkS9xWAUyNYM+HIE25TRZAAKzLLA9BZ527AgD9A/TtS0NQHggwlVL830CMdQV0l9o7HRpduzyGoOZsjfrehWjZocDhLq0jCSQgijFsFjXertCUxPa5JS10hVtCqGmmXAV5dH7pkF5yd16VBM5t6n5kZjmBUjdal6aTaBUUBmMekF502eV0gHKm40NrSP6UE/pmJl/IlolYg+RUQvBP8fiLjmfiL6PBE9TURPEdEP2+i0Fd3AnmlxCKA3Qbv9kV+darzw1IPLpodoTOpSR/7mFJMsHFJF46ZtqgGzgK8pFaOryxaNy89Q02XufeqksIYUncU9VL9/5rRPqeD3A5uFV23SoNFGbJH/hwA8IYS4G8ATiD6esQ3gx4QQrwfwIIB/S0QrlnqNRRd1tWzy/DV639tMUADhUY4qYrvwtDaantlJaFJ0Coc6/SEqRb+thq7ozgs7OlA/g8QGjQNqBkXmwxvHnQKPUOU4UdMmhqEujew2W4pJp1ZCHhdZKRrEggwOxLERW+P/EIBHg58fBfCe6QuEEM8LIV4Ifr4M4DqANUu9xqKTpz4Kj88zNFwanLU1Gi+q97437dke6tLIYrIphgp1qRpJC25cN83ONiXS/wwdiskO+ats1mEigAXyn/ycJLGd7zqneZmeThbq0piDspLYJBZUKehRTLZia/yPCCGuAEDw/+Gki4noLQBKAL5pqddYxqlb6Te4Ex6uYrYYdNIHbQJFgF4riY6ll+EX8+i63O4pprZFVkylqNf73qr4z6By2SYDR36Gih7/+5kjf1Vdpt1DQ11ayN886WCsS32+m3pOuRxp1+vYSOq3JKJPAzga8auf1VFERMcA/A6A9wshIqOtRPQwgIcB4PTp0zofrywh8ldAQjYFG4BeAMdW12Tv+zTUYdqzfaxLA417QxTzhJJBdSrgGxT1TIsBakWzMemmsLa9IU4dcB/wFUJY594DavO9bZGWC0wE6HtDYDFFlyXY0anUtwdWevPCVA+gl7VnK6mzVwjxjrjfEdE1IjomhLgSGPfrMdctAfivAP6VEOILCboeAfAIAJw9e1b99AQNCXvfqyB/S9dUpyuldfZDqRBmMVVSeFQO1KVT7m7K6wK+IVLOYrJA/oBex9d2z67nE6A2L2TMyJ5i0kD+1jSnhqdruFnr1OvI4yKLBjUZgL+pzcIjBPSy9mzFlvZ5DMD7g5/fD+AT0xcQUQnA/wPgt4UQv2+pz1rqGjnWHOgEUONAx6c12QUR1bwMSySky8Mb0gi+LvXgsg3nD+gdsmJ6KD2gF/C1jZmYGGTzRAD1tdWxBCA6yL/jDYwpH8C/HzqFhjcL8rc1/j8P4J1E9AKAdwavQURniejXg2v+MYDvBfDjRPSV4N/9lnqNpR6icZXFYMcVaiF/y/iCzrGRbZmRUDAP7PndOtNrJTiQkA7qslnkOgdodyzy4Yt59fTBEBRYZvuozEH7IKx6KwQOANLtq2XS2WzUUpce8rcDO7Pq6mn+LQEIITYAPBDx/jkAPxH8/LsAftdGD6foVFeOkZDdYlB5mCEPb6hLK7jcG6BmcFxklK7lajJ+MG3bK0WnX4xNPjygfoC2TWsCKarpg7aZKjoeYdva+1RvhSC/jzEAmQiaL1aKidfapOVKXTq9fdYWysa6dJvj2cjcVfjqnHdrnYscZlq49zJ03PuWBWr1dakf6GKLuqpFnTQ783x4QD24PM4bt6GY1MZlW/9RlCdsaaBxm5TIyc9Jkk5Aj3AAkDSxBSC1UkGrt48t7ZP183ck+RyhWlTrQTIuhjIPSgFQCuDYZuDIlD6VSdphmKCAekqfDefvoy61XkympzVJqRXVUljHDeTsgsuziDsB6pW31okAmnUtdmNSp7NalnRgvZRXbsFtQwcCeskUtjJ3xh+QARz3C0+nHWzbGxhXpwJ6yL9p0ZcGmIgvKKYP2iy8WqkAIfz2F0lic1pTqEuRYgpbR9tsaooUk5yndkFztVRF+xRgPa/abl6oz/eOJR1YK6vNQfl9rACI5nkjNjKXxl81W0UaN9NJWinkg8IhFYNsl6mij8Y5Fp5a+qDVwlPUZVud6v+tWmAvTMu1WeSlgtrmyYD8VYuU2t7AuDUBMJ7vKp6uTU0GoHfQj3XcSXFthQDE5lkV9Q6AspE5Nf6ayN9wkecCikk1AGaL7gDV4LIlB6rRIsM/FtB+U0vTZVskJ/9WLVPFjh4Z61LPvbe6h4qxjFbgEZq0JgCCCtWi2j20rcnQCmRbexlqnm54XKTls+r01foj2cpcGn/VlsTt/gClQg4Fw+IQQL0PTsuiaMjXo5dmt2BJWfifk2y8hBBWLbGBCYSXoqttmS0F+M/KG4wwSElhtW1ZAai797bttwHZHE8VIZvrAWRztxlw/lqtJCyzwBTPeuDy0gD10+tsZC6NvyrqahueczutS2XhtSwDo2PkrxJctlvk4x7nKUioP8JI2Blk1ayOJgM3HsZNUhZeMxj3gg1yVTxO1LbqVv6tMhq3nO+qhXJtbxgmKZhITXEOAubHRUqRf5u2qYU0sWVFu68rM/5OpKbYJthHDFalEMqNmlqW9EipkEMhR8pBRCsjqbgYpEG2MZKqweUwMGq1yNUMSpsjCKvYnqDVs0sEAGSthHtuHFAviOpYxp3GaaXJumRNhq3nBKQHsuVxkXZgR+/wHRuZS+OvWhre6duVhQPqxt/mEA0dXT4VY94oDBhz3WlokoUeUaSYbFsTAPqbml0QsaCUPtjs2VF0gHq2T7NnZ5AB9VYI1lW3itltPFSMIvIP6z8y5P8tK6rtj1sMtI9q33Ffl3vUJRuFWXkZeR+JqhpJjoBv2vPi1JUaXLbsfgn4BmI4EqnHidrWSQDqzfFsvU9AvUVGx5L2KeWlp5uSBWbZsgJQT6MO4zMWtM8sT/OaS+OvjPwZONBqUZH2sXSDAX9TS0fjdrncgN/+WMXLYEHjioE9rnz4yc+K1RXUZNgkAtQVNzXbZnVA4BEqZJDY0oRcxRkAACAASURBVIGAWv2CTASwoQPlHEzzMniywNQql22LQif/NkP+jkS1KVS7b8+BqmYWcSw8ldJwDiMJBLRFysJjReOpizwIwlpl4KgFfFu9gT0Vo7ipcVAxYZHSIP152dw/QK2Gpu0NISwTAQA1r5pjvo/PRFCrNbFqLqjRfsZW5tL4qx6vyEH7qJTx+x0yhT3nX0w/1DrMG7dO6UvPVhkfDmKPxtOpGPvce53gsj1Fp04xcaBx+VnJuhiQv8K84AIgKnUZYwBiPi9k8ZqyLobUZtVzJWxkLo2/qkFpMiA8FTeYIzAKBLEMBdTqXztLL8N84eVzhHIhp4TwSgXzAzsA9eByk8Ugq29q9kYyPWA5Gomg/sM26UDdI7ReW+X0hmutMC3XXJcsXkvXZT/fdVpk2MpcGv/xodbpD9N2glYDNziJb+VaDCqVyy2GHHVfV3rcZOxl2C9yFV0c9w9I5+Hblnw1MJlWqjAu6/uXblAk1cXhZXjDEbyEQLZt+3IpKsifzctQqJJusni6anOQQ+bS+EteLQl1DUfy7FQelzuJbw3T0RgMsioat45lKHg0XAtPJWjOlZkFqAWXZ4f87eegCvLnNJJAsvFq9PqBLtuCsnTOnxNYperq+unapm2qfT3qlcu2YmX8iWiViD5FRC8E/x9IuHaJiC4R0X+w0ckhKk2h5M3nQpNJqIujQEnqSkVCnr0b7OtSiS/YHd4upa5QEMXhpZULuaAxWTptYf2sFFoGhO0xGHLvfV3x4+I0kr6upI2GaQ6W0ymmFtu40mslOECBpDlvBuT/IQBPCCHuBvBE8DpOfg7AX1nqY5Ew2JbAj4eTpsKDupIeJp8brIP87QvKlNIULcfk61KjfWx1EZGfBpy6yO2K5AC1gC9XVozKCVucQVggeVx8GWdqwWUi+/leL+VTg7BNb2BtL4DZ9fS3Nf4PAXg0+PlRAO+JuoiIvhPAEQB/ZqmPRcJcWhU0PgskxJCLLP/eGyafrcvRJVL+fTrfat8eA1DbaJoMtI/UlRpcZthoVJIOZmuQ7WsyALUqaT4vQyW4bNepNNRVVkP+tmMC1FvO24qt8T8ihLgCAMH/h6cvIKIcgF8G8NOWuthExSA3uvZ9aQC19sccxSGAOuqSrqWNqKSwthhy1AG1xmRttoWXHF8QQrAVXgEpaDyk6OxjQYAi589FZ80AWKmc8tbs9VnmoMppaD7nzzQHZ5Dtk/pNiejTAI5G/OpnFXX8UwCPCyEupO2+RPQwgIcB4PTp04ofry91JTfYPnIPTBrkJCTEg7omF/lyNfpQax+N562RUL2UR38o4A1GsZw+B0IG1BqTceTeA+ktMjg6lQLB2br5XOKmxmWQVTh/No9QY6OxaYMA+M9qJPyWJZWYz+IImEtdaci/2Rvg5IGava6yWht4W0m9K0KId8T9joiuEdExIcQVIjoG4HrEZX8HwN8jon8KYAFAiYiaQoh98QEhxCMAHgGAs2fPOjvNQKUxWZON81dIs2Na5PK7JgViOXrFAHtjGbHGnwEh+7rSs338mgwe2ifpWXF0Kg11lZN77nDRI+GJcgnzgi/3XmVtDa2zYvbo6g1ijT9HrY7UpUIHLnJw/ooHQNmK7Td9DMD7Afx88P8npi8QQvz38mci+nEAZ6MM/yxFpSkUV5aA/PvEzKLgdzZ9wAFgMdC12032aDi48ckDLpZr0V5G2xtibbFsrcvndpOzYjjScgEfde10+rG/56LoAKSeesVVkKdywhZHgRKgHlzmBCBtb4iDCbq4eHilGBcDKHjbnQdncpiL7V35eQAfJ6IPAHgVwA8BABGdBfA/CSF+wvLznYhKUyiOvjQAsFgp7vm8KGl5PEhIoo5mkvFnKIYC1PqOc6REAgHfGrQ/jqKreoMRBpadSid1XdnuxP6eo52zlLTTvHi9jGQ6i6NACZiMpyWMi2kOqsS4mr0BTtXtqZh6KQ9vMEqkOZtdnk3tnz1wt/VnqIjVNxVCbAB4IOL9cwD2GX4hxG8B+C0bnVyyWClitxuP8Ljd4EaCrrY3sEZ3wJj2SdxomLhxlb7jXGi8Wgoak/VHkU2zxty4vZGsplBMXDnqQHqq4rgrKpOulCBsjQGAqJwox4X85Wc0e/FriwvsLE6srdVCad/vvYF/aMwig65ZyVxW+AL+w0xEyL0BCgxZMeVCHqVCDo1EvtXujFEpcpInj4svACY/L06avYF11TKQfoYqr5FMRshc9AgQbDQzyIoB0gPZXAbZ769EqRQTx/2T872ROt/tdYUefIwuzmc1K5lr4588afzFYJsVAwBLKboa3X44uWxksex/RpJHw1ExCqRnMfWD/i62fWl8Xcl1GVwUHZB+JgJX5TcgT/NKD8JyBc3TNmqOMfm6kmM0HKeTAf66ApKNPxcVI73quLXFOQdnJXNs/Ithj5EoaTAuhoVyspfR6PJkCajQPly60k43Ck814uR2YwwlbxC2AG8wwiCmUI4rCCs/I42KqRbzVuf3TupKq2jnAAWApLPSdHFQMT7YiTP+korhACCLKRuNXHMZ7XMTSJpB5soSAIKNJgGN+8jfXlc+5wey48YlhGDzMtIKhyRCYkl9S0mXHQcrOSmmZF0cBmWhnOwRNpkoCyAImqfUtXB4GEB6cJnP+EuDHL22uFq0AGOvOg5YZbTPTSTptA/fwlsoFxTQuL1BTtPVCw6NYUH+KZy/vLdLLF5G8kYjNzuOe5iWmtsOkb/93PDpwOREAC5jktYygJP2SQsuc+mqlfLIUToan8VGk9E+N5H4aDwlTZGL9knl/HmoGCB5UxujcXsjKbNu4vKR5SJZYtAlN5o4j4bTy5D3JonbLVseGiNlqVpEbzBCL6bdN1eRHJB+whZXNTaQ3PpjMByhNxixjIuIAu8pBvkzxmfSaB/OLLBZyRwb/wK8YfzCa/ZmY5CHIxHoYkL+lWJsZtFuhw+Nlwp+e4I4I7nLiMaXqskLbzcoylqKaWlhokveq326uv3Y1hm6kmZQGl2eLpFAehM0LioGkBlTcRsaTysTKYsJ852TikmLp8l0U67nNQuZa+MPJO3kfKhrMYGKke9zGORQV4xBbjAiZMA3lPGGi0+XNOpxG02jO0COeDj/pTCIGLOpdQYsmwyQPgd3uwMWzwlIP2GLqz0GIDn/GI9QGkm2eFr8HAzjMwzjkinb8R4hXyxoVpIZ/wS+kAsJLVaKaPaiuw9yG+TFSvxGM+bheQzKUrUYou5p4UTjC6UCiBCvKwhic6TlyucQ79HwBOeB8XNIuodcXkbSCVu9wRDd/ohNVz3hONGQHmG8h2kBX651nJSyzVn/MSuZW+O/UI4v2pBte7kW+UKlgOFIRPLjDUZ6BEjOIOHWtVQpxvYRGuuyv4e5nM/tJumSdI2tyM0qiWLi2jzTUhV3u322cdVL8YVyIR3ItdEk0D6ybxIndRYL4MK27O5Ttv3mcjkUGGJBs5Kb55syS1L0vtMfsrTt3a9r/8ThNJKAv9HMIjAKpCD/bh/VYp4lMAoEG00CQuYzyJLzj49lcBnJML4QMQdHQSyIa1zVhKI8qZ8N+Sf02Q89QsbnFWf8+TeaeC+Dsy5oVjL3xj8KTXJPmqQy9AZjBg4QcP7eAKORe4ppqVJI5OG59ADBRpOwqXHpKhfyKBdyCV5Gny8+kxBfaPQGEIIPjScdGL/DbJBrQS+mKE+XfW0l0Jw7nX4QC3IfX9jp9Nme1axkfo1/QtGGC9cUiFnkzMh/sVKEENHufaPrn2fKtRh85B9PxbAa/5SNhstwAf64op6VEGJmAd8xQuYqvPKRf5RXOI7P8CUC+J8b72Xw3UP/WUV5GdIg2zark5JUQ8MZn5mVzK/xTzDIO21+dxGI3mi40XhSSlqj67umXItBUjGR7n2XFwmlBZe5PCfAfxZRhqsnOzdyPauEQPYOY8AcGM/lqA1Uejlc832l6ne93O54+363w7ypLVYK6A8FehFZTDvMBjmpNohb1yxkbo1/aCQjHub2DGkfufC4kGtSZ8/dLh83DvgIzwuKdvbr4qtdAGRWh/uAr9QVaSSZ6ZGkQHaIkJl0rdQCg9x2Py65bnYidfkAhCswmlSUx1mT4euKLyjbbmfG/6aRYj6HSjG61bIr2ifKIDe6AxTz9q2jp3VFjWu3w03FxKcqNjp83DjgbzRReoYjgQZjYNTXFR1f4KYsgKSNRmbg8NzDFWmQZ+BlrAQnu23H6GKdFwnUGT/yL8SmbM8d8ieiVSL6FBG9EPx/IOa600T0Z0T0LBE9Q0RnbPRySVz0njNHHUhutSwbrXHkqANpmUXcyD+ZSuClYvxKzuFUILvJHDORn9WINFy8BXmhrhkg/1opj0KOIg3ybrePUiEXew6uriynbDScm2eSV82ta7HiHxg/3fRvNBLsXsYsxBZufgjAE0KIuwE8EbyOkt8G8EtCiG8H8BZEH/Q+c1mMyYmXWQJc7Vll4UccD89puGT9QlxwmTsIC4yN4qTsMmbFTOqavofu0Hh8fIZdV5RBZgYgRISVWjGG9uH3nPzPjd5oeA1yfL0OdxA2rjZIZmbNm/F/CMCjwc+PAnjP9AVEdC+AghDiUwAghGgKIdqWelkkDnVxZwkU8jnUSvnIICJXO2cp0uWOQl2NHq+uOOTfGwzhDUbsAV9gv0HhRsi+rujMonF8hpfOiosFESMAAXzjtBMRhN3t8BWTAf53zlF8fIGbigH2gx0hREAxude1y0wTz0psjf8RIcQVAAj+PxxxzT0AtonoD4noSSL6JSKK9C+J6GEiOkdE59bX1y2/WrrEnePrgr9bqRajDXJ3ENJCHJLkcvucPy9q9T93ry7u9NU9urrRuni9jCK8wQjdqTx17sAoEH+o0G6nz5qZBfhB38h5wUxZ5HKEpZj57s74791AO/0h+kPhRNf0HOSOEc5KUo0/EX2aiL4e8e8hRR0FAH8PwL8E8F0A7gDw41EXCiEeEUKcFUKcXVtbU/x4c1muRU9QF5H75VopEnVxUzGVol+kNJ1pIURQMcqI8Mbpg1NUjAMjGZc7zk2PAPFBRDcUU3RaqQsOebkaR/vwImTABzvxAV/3cScXBllmTE3bjG3m1PBZSaolEEK8I+53RHSNiI4JIa4Q0TFEc/kXATwphHgx+Js/AvBWAL9h+J3Z5EAMBzpL5M/NgQKI5Hbb3hDDkWDPhwdeW+S/6yTgO9a1tlge6+oMUMrn2DKzpC5ZpDQZ9Ofm4QF/Dj53tbHv/Z1OH6cP1ll1LUfM98FwhJY35EXj5QLyOcJWey+wcmH8DwSU6lYrZqOp3VzG33YWPwbg/cHP7wfwiYhrvgTgABFJKP/9AJ6x1MsiK9USttvevlYIuw5KteOCbVttL5xUXBK18LhL+IGxlxHLwzPeQ7mIp9E456ExUuLOD2gEjda4MrOkrqgMEm4eHvCNU3QQdoBldl37KaYwZsKoi4h8L2NqbUlvihX5h8Vrc0L7pMjPA3gnEb0A4J3BaxDRWSL6dQAQQgzhUz5PENHXABCA/2Spl0VWakWMBNCcaoXgBPnX9rvB3b7fSle6k2y6qqV91ZUSGa3Wecfl58S732jivAy5yGdRv8CdvgrEx2i4C/KkrkZvgP7E4fR+ywo3unam0LirwOhyBLByYZAXK34ge3pcN6vxt1oxQogNAA9EvH8OwE9MvP4UgO+w0eVCQg6vPZ78MktghZ1vLWGnvde9lwb5ALPxX64VcWFzb0KVdFW5dUVx1lstudHw6ZJGd9pIbrU9LDJWjALjjKkoKoEzsAyMn8dWy8OJlWr4vhPvcyJj6uCCT2d1+kMMRoJd13K1MBPvE/Dv4Sxon1yO/LhJxLhK+RyqTHUSs5K5rfAFxothcuK0PX8xuED+3nC0p9Ph2CC7p33CjYbRIAOIzOrYDMa1wjiufI6wVClgu73fo+Ee06RBnpTttsfupckNcrMVtdFwz8H9AUtXqHWl6tM+k5SqK278QK2IrRjkz02drdRKkbqWqnyFmrOS+Tb+sgx94mFy9/UJdVUjdAWGjJ/2Ke5DQtuOvIzVWgkbrf0GealSYOvlL+XgQnmfrs2Wx+phAP7zIAI2pxb5RtPDQe6NJvi8yefV7Q/R8obsFN1yRNsFOR9d0D7TlCr3uQFjXaVYKsYFTTcNQHY6HnvMZBYy58Z//8Lj7ug5rWsS4UkEcYB5kR9cKKPbH+05uMMFGvd1lbDZ6u15z4VBBnyUPI2QXejK5/wg4izGtRoxL+TPkprhkqiGa2Nd/NTjtC4537kp1Sjk73d69TOBuHVFxRduNr4fmHPjH+Vyu3KDDwWLaxK5bjpC43IhbzQnNxoPiw7Q+Gq9jM2Wt6fZ1ZYDesTXtd/4b7U89vsH+Ih8MqWv4w3R6Q+xymwkfboAe4zXpoOYCTDhfU4kA9xo+hvcIW7jHxHI3gh0cY/rQL2ETn+4pyhvwxEAORAxBzPjfxPKSrWIfI7CBQAAGwHa40Zdh4LPu9EY65KcMjcaj9po/JRS/sVwsF5Cfyj2dBHdartZeAfr+ymmzbbHTo8APiKfXOThvHDkZWzt0eU50TWZ4CAlRP513vkeFU+70ezhQK3Ifs6tvE971nGzF645TllbKGO92dsDdjaaHru9mIXMtfHP5QgH6yXcaIwn6HpgnCeLezgkROMTVMKNZg/L1SLKBd4sgdVgIW9MLAaXVAwAbE56Ga0++4YmdW1NeBltb4BufxSOl1tXFBXjQtc0mpR0E/fzWq4WkaO9oGCj6SEfZLFwilw/ew2yGyMZAqvm3o2G25uRurzBKAQ7QgjcaPbY7cUsZK6NP+Aj/MkJeqPZC9EYpyyUCygXcnsm6HrDzaSRSGiS9rm+28NhB7pWp7wMIYSzca3WSxiMRFgsJMfnBPnXS3s2aldUDOAblPUpIwnwo/F8jrBaL4cAB/DByIFaibWHEDA2/pO6XBnkcKPZo8tzgvwliJO6djp99IfCiS7XMvfG/9BCaY/xX2/0cLDOvxiICIemNpr1hhuDfDCC9rne6OLwkgPUNeVlbLf78IYjHF6s8Ota2GtQrje6AIDDS/y6Di9VsNHywoIouWm7MF6HF8u4vtsNX2+0PBRyxJ6mGOpq7N1oXIxpoVxAtZjfu9G4Qv5yownm4GA4wlZ7Nl6GHJ+Le+ha5t74ry2Up9xFz5kLd3ChtAeNrztyF2ulAmql8cLzBiNstftODLLcUK6HBtn//4iDjeZIYOSvBYby2m6gy8G4jiyVIcSYtri609nzHXh1VXC9MeaRpZfmIm/88FI53DQBf3zcmT6AD3bWFsv7kb8Tz2kvGvcTEIA1R7QPMJ4XcsPJaJ+bUA4t7g3grDfcBIoAH3Vdm0B4640e1hzpOrpcwdVd32DdcDhBDy2Ukc8Rru5IgxygcQcG+eiy/5nTupxsNItyowmM/24XK7Ui22lXk3J4sYy2NwwPqrm62wnH6kLXpEG+stPF0aVqwl+Yy9rimM7qeEPsdgdOvLRyIY+lSiHUtR5mMLnwMvYGl8MYYUb73HxydKkCbzAKOd3rja4TKgYAjq9UcXnbN8jN3gBtbxi6rOy6lqu4vO0bR4nGXYwrnyMcWSzjygwM8tHAcFydQP7FPDnh4aXxleO5utML9XPL2KPxn9OVnS6OLbsxyIcXK7jR9DAcCQyGI1zb7eL4iptxrS2UcT0Y0+XAc3Kl6/BSJXxWV4J572IDPVQvo5incG2th2vLzbhcytwb/5MH/EV2abuDbn+Ia7s9nDxQc6Lr+EoVu90BGt1+uAkcX3GzyI8tV3AlWHASKbugLIC9XsZ1h4uhWvIR3pj26eLwYsUZPSJ1yP9d3T+5KV/f7UIIgas7XWfI/8hSGcORn6FyvdHDSMDZRnNspYLL2x0IIcbz3ZGukwequLjl67gU6HKxjnM5wvGVaqjjwmYbi+WCk/iMa5l7439CGv+tTjhB5YbALdLQX9np4tUNv/Ha6VU3G82xlSquN3roD0d4dbMFADjlaFM7tlwNkf/FrTZW6yVUS26aXB1droS6ruy4o0emEd7V3a4z5C/n4MWtDna7vkd4zNG4TgXz7dXNdggOjjlC46dXa2h5Q2y2POdgZ9r4lws5Z0HYEytVXNry1+/FrQ5OrtZuur4+QGb8cXLFXwyXtjvh5DnlyCCfCBbZ5e0OXt10a/yPL1cghI/6X9loY6VWdHbYxPGVCi5tdTAaCbx8o40zB92MCfA3MLlxvnSjhTPMh5BIyeUIp1ZrePlGC63eAOuNHk6tujFcJ1aqKOQIL220cDEwKq7Q+G3B/Xplox1ubK7Q+OmJjebydhc5ckPFAP682On0sdvt49JWBydWqs4M8olJ5L/VdgYWXcvcG/+lagGL5QIubLZD4+/qYUo39JWNNi5stVEv5dk7eko5c8hf5N9cb+LVzTZuc7TJAMCdawvoDUa4uNXByxvuDDIA3HV4AS/daGG328e13R7uWHOn645Dvq4X11uhbhdSyOdwarWGVzZaOH+96VTXiZUqcgS8GugicgdAJIi6sNXBKxstHFuusrcXkSLX1qWtDi5stUNvypWu640euv0hLm51nHnUrsXqSRDRKhF9ioheCP4/EHPdLxLR00T0LBH9Kn0L+UhEhLuPLODZKw08f62BajHvlNtdrZfw7JVdvLjewumDdWfo5NuOLgIAnrvawMsbLfZj+ibl7iO+rqcubePKTjfceFzInWsL8IYj/PXzNwAAdzjUdcdaHS9ttPD8tUao25WcOVjDSzfaeOFaE/kc4XZH4yoVcji+UsXLG208d7WBMwfrzii6UwdqIAJeXG/i2SuNcE66EHm/nrm8i+evNXDPEXe67jmyACGAP//GdbS9IW53CEBciu02/CEATwgh7gbwRPB6jxDR2wB8D/zDXO6Df4j737fUyyr3nVjG05d38OSrW3jDyWX2ToBSiAj3HlvC1y/v4CsXtnH/qWUnegC/j8uRpTI+980NXNjs4PXHl5zpkij1j568DMBfHK7kzkDXY1+9tOe1E11rdXiDEf7smavI5yikTFzIPUcX8c3rTTx1aQdnDtZQYjwneFpef3wJT17YwnPXGnidQyNZLeXxuiOL+MKLGzi/3sS9DufgPUcWUCnm8IdPXkS3P8J9J9zpuu+Ev27/7y++AgC4/+SKM10uxXaGPQTg0eDnRwG8J+IaAaACoASgDKAI4JqlXla578QyWt4QX724g/tPuX2Qrz++hK9f2sVOp483n450lNjkDSeW8Znn1wEA3337qjM9y9Ui7lir49PPXgMR8NY7DjrT9frjS6iV8vjk09ewtljGXQ7R+NvuPAQA+OTT1/CmUytODfLb7jwEbzjCZ55fx/2n3M6L7779IC5sdvDSjZZTIwkAb77tAL7w4iaGI4F7j7nTVcjn8IYTy/jc+Q0A/tx3JScPVLFSK+Jz5zdQyufwOocejUuxnc1HhBBXACD4//D0BUKIzwP4CwBXgn+fFEI8a6mXVR74tvHX/oHXH3Gq679984nw57fddciprn/45pPhz/c5XAwA8NAb/XF9x8kVJ+2cpVSKeXzf6/zn9X2vW2NvwzEpp1ZrIZ3wA68/6kwPALzlzHhzfuj+4051fe8943n3njedSLjSXibX1ttft888sMqD9x0D4NOrdxxyBwqICP/gDb6u771nzSkocCk02Zo08gKiTwOImvk/C+BRIcTKxLVbQog9sIWI7gLw7wD8cPDWpwD8r0KIz0ToehjAwwBw+vTp73zllVc0hmInn37mGjZaPfzwd512rut3Pv8y7lxbcG78B8MRfv2zL+GBbzsc8vKuZKfTx8f+9lW8500nnMVMpFzYbOMvn1/Hu+476ryh1gvXGvjCixv4777zJGolt7ncT1/ewbmXt/A/vPU2p5saAHz2hRu4stPBD5095VQPAHz8SxewtlQON21XMhwJ/OoTL+BdbziKbzvq1qPZbnv4tc+8iA/83du/5Zq6EdGXhRBnU69LM/4pSp4D8HYhxBUiOgbgL4UQr5u65qcBVIQQPxe8/jCArhDiF5M+++zZs+LcuXPG3y2TTDLJZB5F1fjb+iuPAXh/8PP7AXwi4ppXAfx9IioQURF+sPdbivbJJJNMMpk3sTX+Pw/gnUT0AoB3Bq9BRGeJ6NeDa/4AwDcBfA3AVwF8VQjxx5Z6M8kkk0wysRArElMIsQHggYj3zwH4ieDnIYD/0UZPJplkkkkmvHJzhqkzySSTTDKxksz4Z5JJJpnMoWTGP5NMMslkDiUz/plkkkkmcyiZ8c8kk0wymUOxKvJyKUS0DsCmxPcQgBtMX+dmkXkb87yNF8jGPC9iM+bbhBBraRd9yxp/WyGicypVbreSzNuY5228QDbmeZFZjDmjfTLJJJNM5lAy459JJplkModyKxv/R17rL/AayLyNed7GC2RjnhdxPuZblvPPJJNMMskkXm5l5J9JJplkkkmM3HLGn4geJKLniOg8Ee07U/hmFSL6TSK6TkRfn3hvlYg+RUQvBP8fCN4nIvrV4B48RURvfu2+ubkQ0Ski+gsiepaIniaifxG8f8uOm4gqRPS3RPTVYMz/W/D+7UT0xWDMv0dEpeD9cvD6fPD7M6/l9zcVIsoT0ZNE9CfB61t9vC8T0deI6CtEdC54b6bz+pYy/kSUB/BRAO8CcC+A9xHRva/tt2KT3wLw4NR7HwLwhBDibgBPBK8Bf/x3B/8eBvB/zug7cssAwE8JIb4dwFsB/M/B87yVx90D8P1CiDcCuB/Ag0T0VgC/AOBXgjFvAfhAcP0HAGwJIe4C8CvBdTej/AvsPefjVh8vAHyfEOL+iZTO2c5rIcQt8w/A34F/RrB8/TMAfua1/l6M4zsD4OsTr58DcCz4+RiA54Kffw3A+6Kuu5n/wT8s6J3zMm7g/2/v3FWrCqIw/P0QvIvBeEGMIAELG1EQL8QiiFgEsUohCKbwBawEEXwEyQtYF1kgqgAAAnRJREFUioIkgqRRMdqqRKNGFE0gYEjwFJLYKi6LWftwCFHUY/Yms9cHm9mzZor5hznrzG2z2AC8AI6SPvjpcHtznAP3geP+3uH1VHXb/1JnN8nZnQRGAeWs19s+A2xbYit1XGc18wd2A59a8rNuy5WdZjYP4GkRJDW7fvDl/SHgKZnr9i2QCaBBink9DSyY2Xev0qqrqdnLF4GuclvcNkPAZeCH57vIWy+AAQ8kjXvscih5XK9sROryWS7qdR2vM2XVD5I2AcPAJTP7Kv0yuHkWui0FQDooqRO4C+xfrpqnq1qzpDNAw8zGJfUV5mWqZqG3hV4zm5O0A3go6f1v6q6I5txm/rPAnpZ8NzBXUVvK4LOkXQCeNtyeTT943Odh4KaZjbg5e90AZrYAPCGdd3RKKiZrrbqamr18C/Cl3Ja2RS9wVtIMcJu09TNEvnoBMLM5TxukP/gjlDyuc3P+z4F9flNgDXCOFGQ+V+4Bg/4+SNoTL+wX/JbAMWCxWE6uJpSm+DeAd2Z2vaUoW92StvuMH0nrgVOkg9DHwIBXW6q56IsBYMx8Y3g1YGZXzKzbzPaSfq9jZnaeTPUCSNooaXPxDpwGJil7XFd98LECByn9wAfSPunVqtvzH3XdAuaBb6SZwEXSXucj4KOnW72uSLeepoE3wOGq2/+Pmk+QlrevgQl/+nPWDRwAXrrmSeCa23uAZ8AUcAdY6/Z1np/y8p6qNbShvQ8YzV2va3vlz9vCT5U9ruML3yAIghqS27ZPEARB8AeE8w+CIKgh4fyDIAhqSDj/IAiCGhLOPwiCoIaE8w+CIKgh4fyDIAhqSDj/IAiCGvIT8c39JucysTcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_sine(N, A, fs, f0, phi):\n",
    "    '''\n",
    "    N : number of samples\n",
    "    A : amplitude\n",
    "    fs: sample rate\n",
    "    f0: frequency\n",
    "    phi: initial phase\n",
    "    '''\n",
    "    \n",
    "    T = 1/fs\n",
    "    n = np.arange(N)\n",
    "    x = A*np.cos( 2*np.pi*f0*n*T + phi )\n",
    "    \n",
    "    return x\n",
    "\n",
    "# generate signal\n",
    "N = 501\n",
    "A = 0.8\n",
    "fs = 44100\n",
    "f0 = 1000\n",
    "phi = 0.0\n",
    "\n",
    "x = generate_sine(N, A, fs, f0, phi)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用scipy中的ifft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hw/anaconda3/lib/python3.7/site-packages/scipy/fftpack/basic.py:160: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  z[index] = x\n",
      "/home/hw/anaconda3/lib/python3.7/site-packages/numpy/core/numeric.py:501: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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m95pZlZktN7PVZvaymX3XzCryse98SBwVfBWzNSIiIjOXq+D+aGa2CPgQsMrdzwOiwC3AvwCfdfeVQBfwvlzvO1+S46YXSpXggRYRESkHmRHuY+p2HC8GVJtZDKgB9gDXAN8P198D3JSnfedcctxouup1FBERKY7U+IRICZ6Ucx58uftu4N+AnQRBVzewFjjs7olws3Zg0fjXmtntZrbGzNZ0dnbmumlTlgynLoip5ktERKSoMiPcpwvuNbE2mFkTcCOwHFgI1AJvnGDToz4td7/D3Ve5+6qWlpZcN23KkuG0URUlHGWLiIiUg3TNV7rbsRTPyfnodrwW2O7une4+AvwQeCUwK+yGBGgFOvKw77xIZ75UcC8iIlJcmaEmwoSIar4CO4ErzKzGzAx4HbAR+A1wc7jNbcD9edh3XoxOL6S5HUVERIrp6OmFUsVszpTko+ZrNUFh/TrghXAfdwD/AHzYzLYAs4E7c73vfBmdWFtzO4qIiBTT6Dhf6eCrmK2ZmtiJNzl57v4J4BPjFm8DLsvH/vJtfOarFPuXRUREykFmbsdIepDV0ou+NML9JGiEexERkekhNW74J9V8lanxg6wq9hIRESmOTMF9TCPcl7WjpxcqvQMtIiJSDjKZr4jmdixrqXHBVykeaBERkXJQDudkBV+TMFpwr6sdRUREikndjjNEMuVEDKKWrvkqvQMtIiJSDsZ3O6rgvkwl3YlFIkRMmS8REZFiGj/OVynWYSv4moRkyolEIAyyS/JAi4iIlIP0KTiWznxpYu3ylEgGmS8zTawtIiJSTOPH+VLNV5lKuRONWCbzpdhLRESkONKxVkW64L4ET8oKviYhkUoFwVdEmS8REZFiGp1YW+N8lbVkijGZrxI8ziIiImXB1e04MyRTKWIRU82XiIhIkaVjrfTYmxpqImRms8zs+2b2opltMrMrzazZzH5lZi+H90352Hc+JFJOxCwz1ITG+RIRESmOdAIkakY0YiRTqSK36OTlK/P1OeDn7n4WcCGwCfgI8JC7rwQeCp+XhFTKiUWzuh1L7ziLiIiUhXSiyzLBV3HbMxU5D77MrAF4DXAngLsPu/th4EbgnnCze4Cbcr3vfEmknGhW5kvdjiIiIsWR7n1KzzyjzFdgBdAJfM3MnjGzr5pZLTDP3fcAhPdz87DvvEimgqEmTAX3IiIiRZWeWDtiRixiqvkKxYCLgS+6+yuAPibZxWhmt5vZGjNb09nZmYemTU06+FLNl4iISHGlY62IGdGoZYKxUpKP4KsdaHf31eHz7xMEY/vMbAFAeL9//Avd/Q53X+Xuq1paWvLQtKkZH3yV4HEWEREpC+nSH4sE3Y7KfAHuvhfYZWZnhoteB2wEHgBuC5fdBtyf633nSzCxtmluRxERkSLz7MxXxErynBzL0/t+EPiWmVUA24D3EgR695nZ+4CdwNvytO+cG635UsG9iIhIMaWyCu5jESvJibXzEny5+7PAqglWvS4f+8u3RFJzO4qIiEwH2TVfkYhphPtylfTxNV+ld6BFRETKQabmK8x8aWLtMqWCexERkelhdJyvIPOlgvsylUg50UiESPhpKfMlIiJSHNndjrGIkSzBmi8FX5OQSqWvdtQ4XyIiIsWUXXAfjUTU7Viuxk+sXYIZThERkbIwdm5HVHBfrkYzX+HzEoyyRUREyoG7Z87H0UhEwVe5SqRSRKPZ43wVuUEiIiIzVMo90xMV01AT5SuZcqKWPc5X6R1oERGRcpByMsFXML1QqsgtOnkKviZhdHqhMPNVglG2iIhIOUi5Y5luR6MEYy8FX5ORTDoRjfMlIiJSdJ6d+Yoo81W2EmHBvWmcLxERkaJKhQOfQxB8qearTKXGTS+k2EtERKQ4Uk6m21HTC5WxRGrsxNrKfImIiBRH9tWOkYiR0Aj35Wn83I6lGGWLiIiUA88quI9FrCQTInkJvswsambPmNmPw+fLzWy1mb1sZt81s4p87Ddf0kNNxKPBxzWSKL0DLSIiUg6GkykqY8H5WBNrj/VXwKas5/8CfNbdVwJdwPvytN+8SKScaNSIRoyqeIS+4USxmyQiIjIjHRlKUlsRAzTIaoaZtQJvBr4aPjfgGuD74Sb3ADfler/5lJ5eCKC2IkbfkIIvERGRYugfSlBTGQV0tWO2/wT+HkgPvDEbOOzu6YilHVg00QvN7HYzW2Nmazo7O/PQtJPn7kHmK+xgrqmM0j+cLHKrREREZqa+4QQ1YeYragq+MLO3APvdfW324gk2nfCTcvc73H2Vu69qaWnJZdOmLH1Qo5Hgo1LmS0REpHj6h5PUVgSZr1g0wkiy9AZZjeX4/V4F3GBmbwKqgAaCTNgsM4uF2a9WoCPH+82bI2GgVVcVfFS1lTFlvkRERIqkbyjB4uYaAOoqo5nzdCnJaebL3T/q7q3uvgy4Bfi1u78L+A1wc7jZbcD9udxvPvUOBge1Pgy+aipK80CLiIiUg76hJHVht2N9VZzBkVTJZb8KNc7XPwAfNrMtBDVgdxZov6esZ3AEgIaqOBB0O/brakcREZGi6BseLbhvCBMj6URJqch1t2OGuz8MPBw+3gZclq995VPPQHBA0we4pjJK35C6HUVERArN3cOar9HMF0Dv4AjNtaUzhKhGuD+B3jDzVa/Ml4iISFENJVIkU57JfKVLgtKJklKh4OsE0qnMhurRgvs+FdyLiIgUXPqCt3Tmq6F6NPNVShR8nUDPUZmvKMOJ0ivuExERKXXpoZ5qKsZlvkqs5kvB1wkcdbVjZXDfr7ovERGRgkpP71cbnosbqpT5Kku9gyNUx6OZSbXTA7tpfkcREZHCSl/wls58pYMvZb7KTM9AIpP1gqzMl4IvERGRgkqfe+vCc3FdZqgJZb7KSu/QyJjgK5P5UrejiIhIQY1mvsK5HSNGbUW05Mb5UvB1Ar2DiczVFDDaz6xuRxERkcLqz9R8RTPLGqrj9Awo81VWegZGMlc6wujlrSq4FxERKaz0UE/pzBcEF8Qp81VmegfH13yp4F5ERKQY0kNNZGe+6qvi9A4p81VWegYTmaspYDTzpZovERGRwuofSmAGVbGsbkdlvspPz+BIZl5HyMp8DZXWgRYRESl1fcNJauJRIhHLLKuvUs1XWekdHGE4kaIpa7LO+soYFbEIB44MFbFlIiIiM09n7xCz6yrHLGuureDAkWHcvUitOnk5D77MbLGZ/cbMNpnZBjP7q3B5s5n9ysxeDu+bcr3vXNt5qB+AJc01mWVmxoLGKjq6B4vVLBERkRmp4/AACxqrxixb3FzDkaEEh/tLJ/uVj8xXAvhbdz8buAL4gJmdA3wEeMjdVwIPhc+ntV2HBgBY3FQzZvmCxir2HB4oRpNERERmrD3dgyycVT1m2eKm4Pmurv5iNGlKch58ufsed18XPu4FNgGLgBuBe8LN7gFuyvW+c23XBJkvgIWN1XQo+BIRESmYZMrZ2zN4VOZryezgHJ3urSoFea35MrNlwCuA1cA8d98DQYAGzJ1g+9vNbI2Zrens7Mxn0yZl56F+GqpiNNbExyxfOKuafb1DJFOl078sIiJSyjrD8+7RmS8FXxlmVgf8APhrd++ZzGvc/Q53X+Xuq1paWvLVtEnb1dXP4nFZL4AFs6pIppz9var7EhERKYSO7qDHaeGssZmv2soYs2srMqVCpSAvwZeZxQkCr2+5+w/DxfvMbEG4fgGwPx/7zqWdh/qP6nKEoNsRoOOwgi8REZFCSJf7LGisPmrd4uaaTKlQKcjH1Y4G3Alscvf/yFr1AHBb+Pg24P5c7zuXEskU7V0Dx8x8AezpLp0oW0REpJTtCRMeCycIvpY017DjYF+hmzRl+ch8vQp4D3CNmT0b3t4EfAZ4vZm9DLw+fD5tvbi3l+FEinMXNhy1Lt3fXEopThERkVLW3tVPbUWUhurYUevOWdhAe9cAB0tkDM6jf4JT5O6PAnaM1a/L9f7yZd3OLgAuWXr0cGQNVXEWzapmQ0d3oZslIiIyI63v6OGchQ0EHWxjpc/V63Ye5vXnzCt0006aRrg/hrVtXcxrqGTRrKPTmwAXtDbywm4FXyIiIvmWSKbY0NHN+YtmTbj+/EWNxKPG2rauArdsahR8HcPati4uWdo0YYQNcH5rI20H+zncP1zglomIiMwsL+8/wuBIigtaGydcXxWPcu7CRtYp+CpdL+/rpb1rgMuXzz7mNhe2BtG3sl8iIiL59UJ7cK49VvAFcOVps1m3s4uuvumfFFHwNYEfPb+HiMEbz59/zG3OW9RIxODp7YcK2DIREZGZ56kdh2ioirFsdu0xt3nz+QtIpJxfbNhbwJZNjYKvcdydHz/XweXLZzO3vuqY2zVWx1m1rJlfbtxXwNaJiIjMLIlkioc27eO1Z80lEjnW9Xxw7sIGls+p5YHnOgrYuqlR8DXObzbvZ9uBPm6+pPWE277h3Pm8uLeXHQdKZ2wRERGRUvL0ji66+ke4/txj90YBmBl/ePEiHt96kI0dk5pYp2gUfGVxd77w6y0smlXNDRctPOH2bzg3uJz1/menf5QtIiJSih54bjeVsQi/d+aJpx18zxXLqKuM8YXfvFyAlk2dgq8s31/bzrqdh/nLa04nHj3xR9PaVMPvndHCN55sY3AkWYAWioiIzBwHjwzxw3W7+YOLF1FTceKhSRtr4vzJVcv56Qt7+d3LnQVo4dQo+Apt2d/Lp368kcuWNfP2VYsn/bo/e/UKDhwZ4vtr2/PYOhERkZnnrse2M5RI8b6rVkz6Ne+/+jRWzKnl77//PPt6pucczAq+gE17erj1zqeojEX49z+68LgFfeO96vTZXLa8mX//5WaN+SUiIpIjbQf7+MrvtnPDhQs5fW7dpF9XFY/y+Xe8gu6BEW6986lpOeH2jA2+kinny7/dygfvfYYbvvAoSXfufu9lE06kfTxmxqduPJeewQQf/eELuHueWiwiIjIzjCRT/O19zxGPGB9789kn/frzFjXy1VtX0dE9wHWffYRP/2QjydT0OT/P2OArGjG+8rttrN52kFsuXcKPPngV5y069uBtx3PW/Ab+4foz+dn6vXz+oS05bqmIiMjM4e58/P71rGnr4n/+4QXMazj2sE/H88rT5/CTD76a68+bz9bOPqIn0auVbzmfWLuUPPL3r51UAd9k/NmrV7B57xE+++BLJN35m2tXHnNqIhERETnaSDLFx+9fz71P7eIDrz2NGy488cgDx7Nkdg2ffftF0yrrBTM8+MpV4AVB9+O//OH5RAw+/9DLPLOzi0/fdD5LZp+4G7N/OMHW/X3s6xmk88gQ+3uGONg3xMBwkqFEiqFEkuFEimgkQjxqxKMRKmIR6qtiNFbHM7emmgpa6iuZ31hFc03FSdWuiYiIuDsH+4bZ2z3I3u5BDg+M0B3eegZG6BkcYSTpJJIpRpIpkimnIhahKh6lMhahpiLGnLrgXDS3vop5DVWsaKmlKh494b63H+jj7773HGvbuvjAa0/j7647M2c/13TKekGBgy8zux74HBAFvurunynk/vMtFo3wv26+gAsWz+JffvYi1/3nb3n35Uu54aKgWLBvKEln7xAv7+/lpX29bN57hJf29bJzgmLAxuo4tRVRKsNf6Hg0QjLlJFIpRpLOcCJFz8AIvUOJCdsSjxpz66uY31jF/IbgD2DhrOD5gsYq5jdWM7e+clJDapyIuzMwkqR3MEHfUIKRpDOSTDGcTDGSCNqbdCdqRiQCUTOiESMSMSqiEaorotRURKmJx6iuiFIRm7G94SJSJkaSKY4MJjgylGAokQwDFmcklSKRDl5STsSCwCAWiRCLGrFI8P1YWxGjripGXWWMylgkJz0p7s6hvmH2dA+Gt4Hg/vBAZtne7kGGk6mjXmsG9ZUx6qviVMbSbY0QjRjDYZJgKJGibyhBz2DiqNcuaa5h5dw6Tp9bz5nz6zhjXn1mqqBNe3r4wbrdfH/tLqpiUT53y0XceNGiU/55pzMrVIG4mUWBl4DXA+3A08A73H3jRNuvWrXK16xZU5C25cOe7gE+87MX+fHzeyZMd0Yjxoo5tZwxv54z59Vzxrw6FjRW01JfyZy6ykkHIIlkip7BBN0DI3T1D7O/J/jj2dszxL7w8b6e4I+WpbWgAAAgAElEQVRqYNxYZBEjzJRVs6AhCMxa6iupjEUyf+z9w4nwCyTJkaERegYS9Ib3PYMj9A4m6BkYIZHDlG4sYtRURKmtjFFbGXz51FXGqK2MUlcZp64ySl1VsK4+3Cb9OBKxIPBLBP+VDY6kGBhJMjCcZGAkyWDW48x9+HgwfJxIOg6k3Em5405480zAGI9GiMeCLGQ8Mvo4+OyCgDn9n2D6vjKe9TgWpSoebhsffc1wMsXgSJKhsN2DI0kGR4Jlg4kkg2E2dDgZfIGPJIPgNhF+oQfLUyRSjpkRMYiE92OfW6ZN6X0Hz7Mex4JAuCIWoSLMtmY/r4xFxnzew2G7jvV4aCS8T2QvD7K6ieSJf3/MjIqYZdoSz7qvHPc8aGN4fLKXh8etIhoh5WSyykOJ0Xall435GbJ/lvB3K/2zMIlf/VjUwjZFiceMyqzPc7S9o/djfxbLvC4ejZBI+ph2Z5/4MreR5FE/U7B89OcL/mTD32+C3+/gPmhzet/pzzD4/MLnWZ/7mN+Ncb8n2T9nxCzzNzbR3+DgSNDuzO98Yvzvf7B+OBl85uPb7OHPEjE7qi3Z7Uz/TVbFg7+9qtjofbA8krmvjEVJpjz4HhxK0j+coC/8LjwymKB3KPh+7A2DrCND6ccjDI4cHcBMVSximUCsrjJGQ1Wc+qoYDdXBfX1VsKyuKkYq5Zlj39k7xP7eQfaF54P9vUMMJ8a2Kx614J/zxurgn/NZVSxoqGLBrGrmN1TRVFNBY3Xw3pPNHg2OJDlwZIj9vUN0HB5gy/4jvLz/CFv2HWHbgSOMTPD3XhmL8IeXtPLX16487tR+05mZrXX3VZPatoDB15XAJ939DeHzjwK4+/+caPtSD77SDh4Z4rGtB2nv6qeuMsbs2kpOm1vL8jm1VMZOnIbNFXenZzDB3u5BOroH2Jv5L2cg89/O3u7BY2bSaiuCgKehKk5DdZyG8A8/+0ugoSpObWWUimiEWDToIq0Iv6gjBslUcJVpyp1kKsiGDSeCL9b+4eA2MJzIPO4bStAXfukdGRwJv/RGv+Sm0odvBjXxKNUVwRdtdfg4fV8VixKL2piAxQyM4D6V8jGBz3CYes9k+8KfJ/3lNxieTHJZbpA+kcSygov0f8zp5+kvSXcn5elAMv3cSaSC9gYn49GTc6Eu1h1/wo5Fg8/3eFIpMp93OgCa6Es8n2IRGxs0RSNETvB/kjuZwHgkkWIobH+hpAOOTJAdD9ptZhjB30T273j6MIxkgvsw255+nBh9nmujgVF4n/4nJQyWqmLB90nQ7qz2Zz1PuWeC5UygP+55+u9yMDG1YxGNGPVZwVAQAMWD51XBP4Lp5bWVMSrjUeLh32f67zYWMWJRC34/UkFWLP1PVCKVon846/tuXHDXm/7HN+sf4Im+Y+qrYsytr2ReQ1XmPuj9qGZBGGjNqa0saInKSDJF28E+Nu89kun1WT6nhitPm0Njdbxg7ciHkwm+CtntuAjYlfW8Hbg8ewMzux24HWDJkiWFa1keza6rPOWCwVwws0xt2Jnz64+53WjgkCSVgtrKKLUVsWlXP+buDI6kMl9IfeGXkrsTz8oeVMUjmeAqnXUqxoUQiWQq85/7YFZmIjtQGxpJEo9FMiecdDCYfTLKZ/vdnZEwq5LdpvFZn6Gs5yn3TBCSncWpnCATkr0sVz9DKhV04wwnRrvj00HxaIAW/CwjSWck60SczmIG2b/R4CS7rWOyUtFIzv4OPAyAszNpQxO0fSjr50ovy2Scsj/T2Nisana2J19/u+nfl/G/H8PJZFbGbezvSvbfYuafnqy/zWJ8z6T/oRqfZR4KH0cjFmTXK4Lse01FjKp4cb5HjsXdM8FaNPwHIf27MN3EoxFOn1vP6XOPfR6aCQoZfE30mzomVnf3O4A7IMh8FaJRMlY6HQ/T+z8QMwu+vCuitNRXFrs5JxSLRqiLRqirnL7XuGS69WIRSuVrMRIxKiPRaXmSOR4zy1w8Uzv9f30nlP37Qon+DBD8DlVFopMqCJ+uzCxTfiGloZCVze1A9rw9rYBmpBYREZEZpZDB19PASjNbbmYVwC3AAwXcv4iIiEjRFSxH6e4JM/tL4BcEQ03c5e4bCrV/ERERkemgoB3E7v5T4KeF3KeIiIjIdKLRLEVEREQKSMGXiIiISAEVbJDVk2VmnUBbAXY1BzhQgP1I/ulYlg8dy/Ki41k+dCyPbam7t0xmw2kbfBWKma2Z7Ii0Mr3pWJYPHcvyouNZPnQsc0PdjiIiIiIFpOBLREREpIAUfIXTGUlZ0LEsHzqW5UXHs3zoWObAjK/5EhERESkkZb5ERERECkjBl4iIiEgBzdjgy8yuN7PNZrbFzD5S7PbIKDO7y8z2m9n6rGXNZvYrM3s5vG8Kl5uZfT48js+b2cVZr7kt3P5lM7sta/klZvZC+JrPm5kV9iecGcxssZn9xsw2mdkGM/urcLmOZQkysyoze8rMnguP5z+Fy5eb2erw2HzXzCrC5ZXh8y3h+mVZ7/XRcPlmM3tD1nJ9LxeQmUXN7Bkz+3H4XMeyUNx9xt0IJvbeCqwAKoDngHOK3S7dMsfnNcDFwPqsZf8L+Ej4+CPAv4SP3wT8DDDgCmB1uLwZ2BbeN4WPm8J1TwFXhq/5GfDGYv/M5XgDFgAXh4/rgZeAc3QsS/MWfsZ14eM4sDo8TvcBt4TLvwT8Rfj4/cCXwse3AN8NH58TfudWAsvD7+KovpeLckw/DHwb+HH4XMeyQLeZmvm6DNji7tvcfRj4DnBjkdskIXd/BDg0bvGNwD3h43uAm7KWf90DTwKzzGwB8AbgV+5+yN27gF8B14frGtz9CQ++Pb6e9V6SQ+6+x93XhY97gU3AInQsS1J4XI6ET+PhzYFrgO+Hy8cfz/Rx/j7wujAzeSPwHXcfcvftwBaC72R9LxeQmbUCbwa+Gj43dCwLZqYGX4uAXVnP28NlMn3Nc/c9EJzUgbnh8mMdy+Mtb59gueRR2E3xCoJsiY5liQq7qZ4F9hMEwVuBw+6eCDfJPgaZ4xau7wZmc/LHWfLjP4G/B1Lh89noWBbMTA2+JqoL0ZgbpelYx/Jkl0uemFkd8APgr92953ibTrBMx3Iacfeku18EtBJkN86eaLPwXsdzmjKztwD73X1t9uIJNtWxzJOZGny1A4uznrcCHUVqi0zOvrCbifB+f7j8WMfyeMtbJ1gueWBmcYLA61vu/sNwsY5liXP3w8DDBDVfs8wsFq7KPgaZ4xaubyQoJzjZ4yy59yrgBjPbQdAleA1BJkzHskBmavD1NLAyvLKjgqCA8IEit0mO7wEgfZXbbcD9WctvDa+UuwLoDruyfgFcZ2ZN4dV01wG/CNf1mtkVYc3CrVnvJTkUfr53Apvc/T+yVulYliAzazGzWeHjauBagjq+3wA3h5uNP57p43wz8OuwNu8B4JbwCrrlwEqCCyf0vVwg7v5Rd29192UEn/Ov3f1d6FgWTrEr/ot1I7iy6iWCmoWPFbs9uo05NvcCe4ARgv+g3kdQX/AQ8HJ43xxua8D/Do/jC8CqrPf5E4IC0C3Ae7OWrwLWh6/5AuFMD7rl/DheRdDV8DzwbHh7k45lad6AC4BnwuO5Hvh4uHwFwQl3C/A9oDJcXhU+3xKuX5H1Xh8Lj9lmsq5Q1fdyUY7r1Yxe7ahjWaCbphcSERERKaCZ2u0oIiIiUhQKvkREREQKSMGXiIiISAEp+BIREREpIAVfIiIiIgWk4EtERESkgBR8iUhZMLOHzexPi90OEZETUfAlIiXFzHaY2YCZHTGzfWb2tXD+SBGRkqDgS0RK0VvdvQ64GLgU+H+K3B4RkUlT8CUiJcvddwM/A84LFy01s8fMrNfMfmlmc9Lbmtn3zGyvmXWb2SNmdm7WujeZ2cbwdbvN7O+y1r3FzJ41s8Nm9riZXVCwH1BEypKCLxEpWWa2mGAOuWfCRe8E3gvMBSqAv8va/GcEE//OBdYB38padyfw5+5eTxDI/Tp8/4uBu4A/J5iT8svAA2ZWmacfSURmAAVfIlKK/tvMDgOPAr8F/jlc/jV3f8ndB4D7gIvSL3D3u9y9192HgE8CF5pZY7h6BDjHzBrcvcvd14XL/wz4sruvdveku98DDAFX5P0nFJGypeBLRErRTe4+y92Xuvv7w2ALYG/WNv1AHYCZRc3sM2a21cx6gB3hNuluyT8kyKC1mdlvzezKcPlS4G/DLsfDYcC3GFiYx59NRMqcgi8RmQneCdwIXAs0AsvC5Qbg7k+7+40EXZL/TZA1A9gFfDoM9NK3Gne/t6CtF5GyouBLRGaCeoLuwoNADaPdlJhZhZm9y8wa3X0E6AGS4eqvAP/DzC63QK2ZvdnM6gv9A4hI+VDwJSIzwdeBNmA3sBF4ctz69wA7wi7J/wG8G8Dd1xDUfX0B6AK2AH9cmCaLSLkydy92G0RERERmDGW+RERERApIwZeIiIhIASn4EhERESkgBV8iIiIiBaTgS0RERKSAYsVuwLHMmTPHly1bVuxmiIiIiJzQ2rVrD7h7y2S2nbbB17Jly1izZk2xmyEiIiJyQmbWNtlt1e0oIiIiUkAKvkREREQKSMGXiIiISAEp+BIREREpIAVfIiIiIgWk4EtERETyaseBPp5vP1zsZkwb03aoCRERESltiWSKjz+wgW+v3gnAOy5bwj///nmYWZFbVlwKvkRERCQv/vmnL/Lt1Tv506uWk0g5dz++g7desIBXnj6n2E0rqoJ1O5rZYjP7jZltMrMNZvZXhdq3iIiIFNZvNu/nrse288evXMb/85Zz+Mgbz6K5toKvPb6j2E0rukLWfCWAv3X3s4ErgA+Y2TkF3L+IiIgUwOBIko/fv57T59bx0TedBUBVPMrbL13Mg5v2cbh/uMgtLK6CBV/uvsfd14WPe4FNwKJC7V9EREQK485Ht7Pr0ACfuvFcKmPRzPKrTp+DOzzf3l3E1hVfUa52NLNlwCuA1eOW325ma8xsTWdnZzGaJiIiIqegd3CEOx7ZxmvPbOGVp42t7Tq/tRGA53bN7CsfCx58mVkd8APgr929J3udu9/h7qvcfVVLy6QmBhcREZFp5O7HdtA9MMLfvP6Mo9Y1VMU5raWW55T5KhwzixMEXt9y9x8Wct8iIiKSX90DI3zld9u49ux5XNA6a8JtLmydxXPth3H3Ardu+ijk1Y4G3Alscvf/KNR+RUREpDC+8cQOegYT/PW1K4+5zTkLG+jsHaKrf6RwDZtmCpn5ehXwHuAaM3s2vL2pgPs/JZ29Q4wkU8VuhoiIyLQ0lEhyzxNtvHrlHM5b1HjM7VqbagDY3TVQqKZNO4W82vFRdzd3v8DdLwpvPy3U/k9Fz+AIl376Qf71F5uL3RQREZFp6f5nO+jsHeLPXr3iuNu1NlUDsPuwgi85jqe2HQJ0dYaIiMhE3J07f7eds+bX8+qVxx+9fuEsBV8KvibhyW0HAXjFkqYit0RERGT6eXTLATbv6+V9Vy0/4byNTTVxquNRdTvK8T25PQi+KmL6uERERMb7xhNtNNdWcMNFC0+4rZmxqKma3Yf7C9Cy6UnRxAn0DI6woSMYjmwmXxYrIiLTw97uQTp7h4rdjIy93YM89OJ+3raqdcxo9sezcFY1HYcH89yy6StW7AZMd8/sPEw65kop+BIRkSLpGRzhoz94gZ+8sAeA265cysffei7RyPG7+fLtu0/vIply3nnZkkm/ZtGsatbvnrkDrSr4OoG1bV1EDFIe3ERERAqtfzjBe766mg0dPfzla0+nq3+Ye55oY8nsWt531fKitSuRTPGdp3fy6pVzWDq7dtKvWzSrikN9wwyOJKmKTy5bVk4UfJ3AurYuzl7QwJb9R0gp+hIRkQJzdz7ygxd4YXc3X3r3JVx37nwAtnX28cWHt/Kuy5cULYB5eHMne7oH+cRbzzmp182uqwTgYN8wi8KrH2cS1XwdRyKZ4pmdXVyytImImbodRUSk4H6+fi8PPNfB31x7RibwAvira1dy4MgQDzzbUbS2fWt1Gy31lbzu7Hkn9brm2goADh0Zzkezpj0FX8exeV8vfcPJMPhSt6OIiBTWkaEE//SjjZy9oIG/uPq0MesuX97M/IYqfv3i/qK0rb2rn4df6uSWSxcTj55cODE7DL4O9k2fCwcKScHXcaxr6wLg4iVNRCLKfImISGF97sGX2NszyP9303nExgU4ZsbVZ7bw2JYDRZn+7jtP7cKAW06i0D4tnfnq6lfmS8ZZ29bFvIZKWpuqiZih2EtERAplW+cR7npsB7dcuphLlk48yPfVZ7bQO5TIJAsKZSSZ4rtrdnH1mXOnVLOVDr4OqttRxlvTFtR7mVnY7ajoS0RECuNzD71MRTTC31535jG3uXJFMJXPup2Fnf7uwY376Owd4l2Xn3zWC6ChKk40YhzqU/AlWQ4eGaK9a4CLFs8CUMG9iIgUzOa9vTzwXAe3vXIZLfWVx9yusSbOolnVbNzTU8DWwbef2snCxiquPnPulF4fiRhNNRUKvmSsTXt6ATh3YSMQ9K2r4F5ERArhs796idqKGH/+mhUn3PachQ1s7CjcgKU7DvTxu5cPcMtlS05pgNfZtQq+ZJyNe4Jf5LMXNAAQMU0vJCIi+ffi3h5+vmEvf3LVcprC2qjjOWdBA9sP9DEwnCxA6+Dep3cSjRhvv3TxKb1Ps4IvGW9jRw8LGqsyRYERM1KFv5hERERmmDse2UZ1PMqfvGrZpLY/e0EDKQ+GR8q3oUSS761p59qz5zKvoeqU3qu5TsGXjLNxTw/nLmzIPFfBvYhI+Xhq+yH+6MtP8KrP/JpPPrChKEM1TKTj8AAPPNvBLZctZlbNibNeAGcvqAdg89781339YsM+DvUN867Ll57yezXXVHBQwZekDY4k2drZxzkLRoMv1XyJiJSHHz/fwTu/8iTth/o5Z2EDdz++g4/84IViNwuAux7djsNJzde4aFY18aix42B//hoW+taTbSxpruGq0+ec8ns111bQPTAybQLfQlLwNYGX9vWSTDnnZGe+Iqr5EhEpdet2dvHh7z7HK5bM4ud/8xq+cusq/vw1K/jBunY2dhT2isHxuvtHuPepnbz1ggW0NtVM+nWxaITWphp25jn42rL/CKu3H+Idly0hcgqF9mmz64LM3uH+kVN+r1Kj4GsC6T/AcxY0ZpZpqAkRkdLWP5zgQ/c+w/zGKr5y6yoaquIAvP/q06mvivG/H95S1PZ9c3UbfcNJbn/NaSfeeJyls2vYcbAvD60a9e3VO4lHjbetas3J+2Xmd5yBXY8KviawoaOH+soYrU2jo/ZG1O0oIlLS/vPBl2nvGuDf3nbhmHqqxpo4N1y4kN+8uJ/BkcJcMTjeUCLJ1x7bwe+d0TKm12Wyls2upe1gf956aAZHkvxgXTtvOHc+c+qOPe7YyWiewfM7KviawMY9PZy9oGFMWtVUcC8iUrI2dHRz56PbueXSxVy2vPmo9deePY/+4SRPbjtYhNbBT57fw4EjQ/zpqydf65VtSXMNR4YSeStg/8nze+geGMlJoX3a7NogiFPmS0ilnBf39GSuHknT3I4iIqXJ3fn4/RtoqonzkTeeNeE2V542m+p4lIc27S9w6wL3PL6D01pqp1zIvmxOUCPWlqe6r28/tZMVLbVcseLowHWqmmqDbt8uBV+yp2eQvuEkZ8wfH3wp8yUiUooe2rSftW1dfPj1Zx5z+IaqeJRLlzfz9I5DBW4dPLOzi+fau7ntlcswm1oh+5LmWgDa8lD39eLeHta2dfHOy5ZMuX0TaapJdzsq+Jrxtu4/AsBpLXVjlqvgXkSk9KRSzr/9cjPLZtecsFD8/EUNvLz/SMHrvu55fAd1lTH+4OKpF7Kna5R3dw3kqlkZ3169k4pYhJsvyU2hfVo8GqGxOq5uRwkupQU4fe7Y4EvjfImIlJ4fPd/Bi3t7+ZvXn0E8evxT3vmLGkmmnE0FnKS6s3eIn7ywh5svaaWuMjbl96mKR2mpr6Q9x8FX31CCH67bzVvOXzDpQV9PxuzamTnQqoKvcbZ2HqGxOs7scfNpaW5HEZHSkkw5n3voZc6aX89bL1h4wu3PWxQML7R+d+Emqb73qZ2MJJ1brzz1QvbWpmraD+e25utHz3VwZCjBOy9fktP3TWuureDQkZMPvnYfHijaxRG5oOBrnC37j3D63Lqj+rU11ISISGn55Ya9bOvs4y+vOX1Sg4IumlVNU02cFwoUfI0kU3xrdRuvOaOFFeNKXaaitakmp5kvd+ebq9s4a349lyxtytn7ZmuqraCr/+SDr0/9aAMfuveZPLSoMBR8jbO1s4/TWmqPWq6CexGRoz2zs4u3f/kJLvjkL3j/t9bSOzg9Rit3d774260snV3DG89bMKnXmBlnzQ/qvgrh5+v3sq9niD9+ZW6Gb2htqqbj8ADJHGUKnmvvZv3uHt51xdKcFtpnm0q34+BIkkdeOsBwCU9LpOArS+/gCAeODLF8ztH/gajmS0RkrF9t3Mfbv/wkOw/1c9258/nlhn3c/vW1OTv5n4rHtx7k+fZu/vw1pxE9ialwVrTUsq2zryBlJvc8voOls2u4+oy5OXm/1qZqRpLO/t7BnLzfN59so6Yiyk0XnbjLdqqaayvo6hs+qc/7iW0HGRhJkpoGv2dTpeArS3p8lKWzj55TSzVfIiKj1u/u5oP3ruPsBfX89EOv5t/ediGfuvE8nth2kAc37St28/g/D2+hpb6SP7h40Um9bvmcWroHRujK83yD63d3s6ati/dcsTQn8yQCmfkgc9H1eLh/mB8918FNr1hEfTgNUz601FeSSPlJfd4Phb9fpXxKVvCVZeeh4wVfGmpCRARgYDjJh77zDLOqK/jqbZfSFF6g9EerWmltquaOR7YVtX3P7TrMY1sO8qdXLacqHj2p164Iy062H8hv1+PXn9hBdTzK21Ytztl7poebaO869aL7769tZyiR4t05HNF+IvMaqgDY2z25bJ278+twINxSPicXLPgys7vMbL+ZrS/UPk/WaOZropovI1W63csiIjnznw+9xLbOPv79jy6kpX50nr9YNMJtVy5jbVtXXgb7nKwvP7KV+qrYlK7QS5edbOvMX/u7+oa5/9kOfv/iRTRW5y6rtGhWGHwdOrXMl7vz7dU7uXjJrCnNM3ky0sHXvkl2lW7c00NH9yCzaytKuhSokJmvu4HrC7i/k9Z2sI/ZtRUTjrWiuR1FRGD7gT7uenQ7f3hxK6+aYCqc150d1C/97uUDhW4aEAxB8PP1e3nnZUum1F3W2lRNLGJsP5C/4Os7T+9iKJHitiuX5fR9czXW1+NbD7LtQB/vviK/WS+AeQ1B8L5vkpmvhzbtxwyuPnNuSZ+TCxZ8ufsjQOHnbTgJbQf7J+xyBM3tKCIC8P/+eCOVsSj/cP2ZE65fPqeWRbOqeeSlzgK3LPCNJ9oAeM8Ux82KRyMsaa7JW/CVSKb45pNtXLliNmeOm8YuF3Ix1tc3n2yjqSbOm86f3FWip2JufZj56hma1PY/eX4PlyxpYm5DZUmfk6dVzZeZ3W5ma8xsTWdn4f9wdx7qn7DLESASUeZLRGa2377Uya9f3M8HrzmduWF30XhmxmvOaOHxrQdJFHgogIHhJPc+tZPrzpmfKT6fiiWzazI1wLn24Kb97D48wG2vXJaX9z/Vsb729Qzyy437eNuqxSddLzcVFbEIc+oq2Ntz4szX5r29bN7Xyw0XLSz54Z+mVfDl7ne4+yp3X9XS0lLQfQ8nUnR0D7C4+diZr1I+0CIip8Ld+fdfbqa1qZr3vmr5cbe9dFkTR4YSee26m8h/P7ub7oER3vuqZaf0Poub8hd8ff2JHSxsrOLas3MzvMR4pzrW17eebCPlzjsvy8+I9hOZW1/F/kkEXz96roOIwRvPW1Dy5+RpFXwV076eQdyhNSxYHE/jfInITPbQpv08397Nh65ZSUXs+KeOcxcG0/RsLOAcie7O3Y/t4OwFDVy2vPmU3mtJcw29gwm6czzcxEv7enl860HefeVSYieYZ3KqTmWsr8GRJN9cvZPXnTWPZXMm7gXKh/mNVSfMfLk7P3q+g1eeNoeW+sqSPycr+ArtPhykaRceI/jSOF8iMlO5O5998CWWzq7h9ycxbtaKlloqYhE2dhQu+Hpi60E27+vlva9cdsqjsS9uDs4Duc5+3fP4DipiEW65NH9ZpVMZ6+v+Z3dzqG+YP7lqWY5bdXzzGipPWPP1wu5u2g7289YLgzq09NBopXpeLuRQE/cCTwBnmlm7mb2vUPuejN1d6eBr4joGze0oIvnm7vQOjky7E8qvNu5jQ0cPH7pmJfFJZGzi0QhnzqsvaObra4/voLm2ghtyMBp7uvxkVw7Gy0rrHhjhv57ZzY0XLqQ5HBctHxaHY32lh06aLHfnzke3c9b8eq5cMTsfTTum+Q3VHOwbYnAkecxt/uuZ3cSjxhvOnQ8E52SgZM/LR4+pkCfu/o5C7WsqOiaR+Srl/mURmd4e3LiPTzywgd2HB7h4ySz+448uKmjXz7Gk50hc3FzNjScR2JyzoIEHN+3D3fM2L2DarkP9PLhpH++/+rScFImng69cZr6+t2YX/cPJvBXapy1priEeNbac5PyUj205yEv7jvCvN1+Q9+M13ulz63CHrZ1HMl3W2QaGk/xgbTvXnTufWTVB4JrOfKXciVLY9uaCuh1Duw8PMKeu4ph/uKXevywi09d9a3bxp19fQ31VjA+9biVbO/v4wLfXMZwo/sjOa9q6eGbnYW5/9YqTqlM6c349B/uGT3rS5Km45/EdRMx4zxXLcvJ+DVVxZtXE2ZWj4CuZcu55YgeXLWvmvEVHBxe5FItGWDa79qSDr7se286cugreemH+5nE8ljPnBwPbbt7bO+H6Hz3fQc9gYsxo+5bJfJXmiVnBV2j34YHM6MATUc2XiOTDkylA1FIAACAASURBVNsO8pEfPM+rV87h/r98FR9+/Rn8680XsKGjh2+vbit28/jSw1tprq3g5ktObhqc5WHWbkeer3jsG0rw3TW7eON585nfOHHZyFQsac7dFY+/fnE/uw4N8MeneBXmZJ0+t46tnZMPvrZ2HuHXL+7n3VcsLcjwEuMtnV1LRTTC5n0TB1/ferKN0+fWccWK0Qsp0t2OpXpaVvAV6jg8cMwuR9BQEyKSe90DI/zVd55h2exavvjuS6iMBSe+686dzwWtjXzn6V1F/afvpX29PPTifm67chnVFSd3Uk53meZ7uIkfrmundzBxysNLjLf4FMfLynb349tZ2FjFdefMy8n7ncjpc+toO9jHUOLYNVTZvvjwVqrikYKMaD+ReDTCipZaXpog8/VCezfPtXfzrsuXjOkOze52LEUKvggyWh2HB1nQeKLgq4CNEpGy9x+/3Exn7xD/ectFR01r9rZVi3lxby/rdxeuaH28Ox7ZRnU8yq1TGC2+tamaaMTYkcc5HlMp5+7Hd3BBayMXL2nK6Xsvbq6hvat/yuNlpW3e28tjWw7yniuX5W14ifFOn1tHymHHgRNn7nYd6ue/ntnNOy5bwpy6yhNuny9nza+fsNvxrse2Ux2P8gcXt45ZXuoF9wq+gJ7BBAMjSRYcJ2WtuR1FJJfW7+7mG0+28e4rlnJB66yj1r/1ggWYwUMv7itC62BP9wD3P7ubt1+6mKYpXJ0Xj0ZY3FSd18zXo1sOsLWzjz/OwfAS4y1uDsbL2jeJwT+P5+7Hd1AZi3DLpSfXbXsqTp8b1FC9uPfEgfuXfruVqBm3v2ZFvpt1XOctaqSje5CdWVdpbu08wv3P7uY9Vy49agJyU+ar9KX/uOYdJ/jS3I4ikiuplPOP96+nubaCv71u4jkSZ9VUcPb8Bp7aXpwpcb/+RBvJlPO+q44/mv3xLJtTy/ZJZF+m6muPbWdOXSVvviD3cxAuSQ83cQp1X4f7h/mvZ9r5/VcsmlIAO1VnzKunOh7lmZ2Hj7vdnu4BvremnZtXtR6356cQ0kNI/PiFDiDokfr0TzZRFY9OGBhmar6Kf03KlCj4Iiv4qj92ylVDTYhIrvx8w16e2XmYf7j+rKP+o8922fJm1u3sKvhVj9lzJB5ryrXJWDa7lraDfXmpW9t+oI/fbO7kXZcvydTK5dLiplMfbuK7T+9icCSV9+ElxotHI1y0eBZr27qOu92//eIlAP7i904rRLOOa3FzDRcvmcX9z3SQTDn3rdnFr1/c//+zd9/hjVZX4se/V+699z699z5DJ/SekEDokEBI2WWTzQbyyxI22d1skt1kyaYACQydgdD7AEMZpvde3XvvVZZ0f39INmbGRbKkV5LnfJ7Hz9ivpFfXfj3S8b3nnsOPLpo+7HKo5HxNALVt9uBrtJ0yknAvhPAEq03zuw9PMCU1+rQ8llMtL0ikt9/Goeo2g0Zn98a+Klq7+93enZefFEm32UpD5+jVy8fjqS2lhAQpblrhnWrxmfERmBRUjDPp3mK18fTWMlZMSmRmRqyHRze2xXkJHKlpp6vPMuzth6raeHVvJXeszncrwPakm1fkcbyug6/+ZQsPvHqQVZOTuH2EwNVkklITAa++w/7CkBozWs6Xwhag05tCCP/xxr4qCus7+eFXphFkGj1PaXGePYl83xjLR56ktWato0ficjd7JOYl2Xc8eqpe1oCO3n7+vquCK+Zljvq67Y7QYBMZcRGUj3PDwDsHa6hq7eGuNb7JpVqcn4DVptlTfvrs18CSXkJkKN89b4oPRje86xZlc/+lM2jtNnPNwiz+dtuSEf+PqABPuDeswr0/q2vvJTY8eNSt1FLnSwjhLovVxv9+dJJZGbFc4shxGU1KTBiJUaGcrB++/pE3bC2290j8zVfdr3Q+tFL84jz3Armh/r6rki6zdcRZEU8pSI4a14YBrTWPfFbMlNRoLpiR6oWRjW15QSJRoUG8tb+as6amfOm2N/dXs7W4iV9cPXvUZW9f+M45k/mOE8ug0ttxAqht6x2zOJ+UmhAicLR0mTlU1TbikouvvH2ghvLmbu67cOrgsslolFJMTY0esfK3N6zd7LkeidkJESjlep/B0dgc1eIX5cYzP+f0XaKeNCU1msL6Tpff4D8/2cjRmnbuPnuSU9fZGyJDg7l8XgbvHKih2/zF/4Oq1h4efOMwC3Pj+eYy7zX49jYpNTEB1HX0kRY7RvBlCty1ZSHOFPYZhyJW/dfHXPF/mzj/fz5l7zDLLr4wMLapqdFcONP5YpvT02M4Ued6ADAeAz0Sb1yW45FK5+EhQaTHhnu0R+Inx+spa+rmjtXj34XprMmp0XSZrdS0uVZu4tGNRaTFhrnUC9Mbrl+SQ5fZymMbiwH7HyV3PbkTm03zP9fPN6zumDdIwv0EUNfWO2bwJb0dhfB/v37/OP/13jHOmprMwzcsICTIxL3P7qHH7Fylb2/69HgDx2o7uOecyS7NhkxLi6Gzz0K1iwHAeAz0SPRkpfOcxEiP5nyt3VxKemw4l8wZe9nWXVNS7PWyXOmTeLCyjc2FTdy1psAruzBdsSQvgWsXZvGHDSf50Uv7ueL/NlHc0MUfb1rEJMf3Fqikt2OAs9k0jZ19pI5SZgIk50sIf/fa3koe+ayIm5bn8sjNi7l6QRa//8YCatt7+evnxb4eHn/5rIjMuHCucrFx8fT0GACOO1Ew0x1DeyR6suaTJ3sknqzrYFNhI7eszCPEgFmbgWKlrgRfj2wsIiYsmBv9YElPKcUvr5nDNQuyeO9QDelx4bx4zwrOmZYy9oP9XKD3djzjE+7bevqx2PSYbRWk1IQQ/quuvZcHXz/MsvxEHrpq9uDM0tL8RM6dnsK6HeX84PwpHq+C7qzdZS3sKGnmX6+YRWiwa0HDZMcMRXFDF+fP8Mbo7F7dW+WVHom5iZHUtffR2291eylzraNavFGBTXJ0KHERIZx0Mvg6WdfBuwdr+M45k4kJ949E9uiwYH73jQX8ztcD8TBZdgxwjY76M0nRo1cfloR7IfzXQ28exmy18ZuvzTttRuTKeZlUt/Wyv9LYWllDPfJZEfGRIeNqMZMQGUJMeLBH86ZOZbNpntxc4pUeiXlJ7leKB3u1+Ff3VHLNgiwSDaoWr5RiZkYMh52ss/a/H50kMiSIb5/l21Y9ZwJJuA9wA8X/UsaY+ZLejkL4p4+O1PHeoVr+4YKp5CdHnXb7hTPTCDYp3jtU44PRQXFDJx8eqePWFXlEhbm+2KCUIi8pklIP7hg8lXd7JLpfKR6+qBbvbuFXVy3KTeBIdTu9/aPnDR6ubuOdgzXctabAsODwTCa9HQNcU6cZgCQnlh0D9BoLMWGZLTZ+8fYRpqVFjzjbEBcZwtL8RDadbDR4dHZPby0jJEhx88rxJ7HnJUaNu9inM4zokehO8OXLavGLchOw2DQHxpg5/f2HJ4gND+YumfUyxBc5X4H5xnzGB18Dy47JYy47Bm6ELcRE9eKuCsqbu3ng0pmj5lItzI3neG3HmLMXntbuqMR+pZuV2POSIqls6cFi9XybDW/3SEyKCiUyNMit4OvDI3VUtfYYUl7iVAtz7bXEhqsUP+CzEw18dLSee86Z7HdFSycqWXYMcE2dZkwKEiKdyfkK0KssxATUY7byfxtOsjQ/gXOnj757a35OPBabdjp3x1NeHqjE7uZSWV5SJBabprrV8+UmvN0jUSll3/HoxrLp3zaVkJMY4VJ9NE9Jig5jUnIUW4qahr29z2LloTcPU5AcxbfOMj44PFNJwn2Aa+zsIzEqbMy6O1LnSwj/8tTWUuo7+viXS2aMmae00FEJfV+FccGX1VGJfXFeAvOy3avEnptoz2Ura/bs0mO7AT0Swb1yEztLm9ld1sK3z5o0Zi9Mb7l4TjqbCxtpGqZB+N8+L6GksYt/u2q2z+t6nUkG63wFaM9lCb46+8ZccgSp8yWEP+lxVO0+Z1oKS/PH7hmYGhtORlw4+yuMa1D96WAl9ny3z5WfbM+b8mSbHviiR6Kny0ucaiD4so3jL9hHPi0iMSqU6xe7vlPUU66an4nVpnn34Jc3bRyqauPhDSe5bG46Z0+A2lmBRGa+Alxjp5mUMQqsgpSaEGcerTUHKltZt6Oc4gbni0wa4cWd5TR3mfn++VOcfsysjFhO1BnbIzE9NpyLnWigPZa0mHBCg00eLTdhtWme2uKZmbmxTEqJps9io6q1x6XHHa/tYMOxem5bmU9EqO9mlWakxzArI5ZHNxYP9kmsbevl3ud2kxgZyi+vnuOzsZ2pAr3IqgRfnX0kObEtWBLuxZmkt9/KD1/az1V/3Mz9rx7kK7/fyAeHa309LAD6rTb++nkJS/MTnJr1GjA5NZrixi6sBvwV5elK7CaTPW+qtNFzy46fHKunvNkzM3NjmZ5uLxTravD76MYiIkKCuNWNnaKeoJTi51fOorKlh/vW7ePvuyr46l+20NLVz6O3LB5zt7zwPJPjv1Wgvi+f0cGX1tqx7Dj2fxzlKDUhS49iorPZNPet28dre6v4h/On8ME/nc2crDh+8MJeag3oLziWN/ZVU9Xaw73nTnbpcZNTojBbbFS1uDb7Mh7eqMSe58E2PQBrt5SQEeeZmbmxTE1ztEhyIfiqau3hzX3V3LAshwQ/qJu1fFISD1w6g0+O1/Pjlw8QFmzi2W8tZ36Od2cNxfACvbfjGd1eqNtspbff5tRfLUOnOH3UoUQIQ/zxk0LeP1zLg1fM4s419t1bf7xxIef89hPWbinhgUtn+mxsNpvmkc+KmJEew3nTU1167ECbnqKGTnIdVde9oa273yuV2POS7DvutNZuF0I9XtvB5sImfnzxdEN6JMaGh5AZF86JWueDr79utPfj/JYf1c2655zJXL0gi9YeM5NTog352YnhSamJAOZsjS8I/OQ+IZyxv6KVhzec5JoFmYOBF9irlF86N4Pnt5XTYza2VtZQHx6to7C+k3vPnexyADI0+PKmdTvLvVKJPS8pkp5+Kw0dp++4c9WTW0oICzbxTQObP09Lj+FEnXM/+5q2Hp7fXs51i7LIivdck29PSI8LZ0Z6rARePjbwnhyoq1Fn9G9Po6O6fbIzCfemwI6yhRiLzaZ58I1DJEWF8otrTk8gvn5xNh19FnaUNvtgdHaPflZEbmIkl891vRJ7QlQoiVGhXg2+vFmJfWC2rszNpceWLjOv7qni2oVZhi7nTU+LobChE7Nl7NoAf/y4EI3mB+dPNWBkIhDJzFcAG5z5inIm58v+r8x8iYnq5T2V7K9s44HLZhAbfnqV7uUFSYQGm9h4osEHo7PPyu0pb+X2VfkEj3PWYVJyFEUN3mvT89FReyX221d5vthmfpKj1peb5SbW7aygz2J8j8SFufGYLTYOVo1ea62iuZsXd1Zww9Lcwb6QQpwq0N+TJfgCkmOcWXYM7G2tQoymvbef37x/jEW58VyzIGvY+0SEBrG8IJHPT/om+Fq7uYTosGCuX5I97nPkJkZS6cGk9VOt3VxKVnwEX5nl+UrsWfERmBSUudHj0WK18czWUlZNTmJGurE9Egd2pu4oGX3m9L8/OI7JpPjeec6XERFnHlOAJ9yf0cHXYFNtJ2a+JOdLTGSPfVZMY6eZf7tqzqi5VKunJHOirnPwDxej1Lf38s7BGr62OJuYYWblnJWbFElNey99Fs/nrR2ubmN7STO3rcrzSiX20GATmfERbs18vXeoluq2Xm5fle+5gTkpKTqMySlR7CgZvk0PwLbiJt7YV813zp5Eepz3Ku6LwBfoEyJndPDV2NlHbHjwqA15BwR6lC3ESJq7zKzdXMLl8zKYmx036n3nOW4/WtNuxNAGPbutDItNux005CZGojVeKTfx1JZSIkKC+MYS7yWx5ydFjTvnS2vNoxuLmJQcxQU+6JEIsKwgiV2lLcMGv/1WGw++cYis+AjuPVdmvcToAn1CxNDgSyl1iVLquFKqUCl1v5HPPZymTrNTyfYwtKaIN0ckhPEe21hMd7+V+y4YO7l5liOJ/HC1ccFXb7+V57aXc/70VPKTo9w6V64jh8iT9bIAmjr7eH1fNdctyiIucvwzc2PJTYqkfJzLjluKmjhU1c7dZ/uwR+LsNDr6LGw4Wn/abY9vKuFEXSc/v3KWT6vZi8AQ6O/JhgVfSqkg4E/ApcAs4Eal1Cyjnn84DZ19TiXbQ+BvaxViOI2dfTy1pZSr5mcOFsIcTXxkKFnxERwxMPh6a381TV1m7ljtfhL7QPBV4eHga93OCswWm9eX8/ISI2np7qetp9/lxz7yWREpMWFcs3D4nD4jnDU1hcy4cF7cWfGl4/sqWvmfD45z8ew0r+TLiYlHZr6ctwwo1FoXa63NwDrgagOf/zSNnX1OJdtD4G9rFb5jttiTnH/y8gHe2Fc1rubC3vL4phJ6LVb+wYlZrwEzM2I5YtCyo9aatZtLmZYWzeopSW6fLyUmjDAP90jst9p4ZmsZZ01NdiqAdUeeY8djuYt5X4eq2vj8ZCN3ri4gPMR3s0pBJsU3luby2YkGPj1un/06XtvBXU/uJC02nN98db7bBWTFmeGLnC//eT11hZEV7rOAoX/uVALLDXz+0zR1mp1qLQSBH2UL32juMnP72h0cqGwjJiyYF3dVcKS6nQcu812V+AEdvf08u62MS+ekDxYgdcaszFg+PlZHb7/V62/kO0tbOFLTzn9eO9cjb8pK2XskejL4evdgDbXtvfzndd5vrpyfbJ+5K2nqGjM/b6jHNhYTHRbMN5cbV1R1JPecM4l3D9bw/ef3cs60FDYcqyM6LISn71zm1SVbMbEMToiMXTbOLxk58zXcK+eXIhml1N1KqV1KqV0NDd7fzv7QVbO4eoRt9acK9D5Swni9/VbuWLuDY7UdPHLzIvb//CJuXJbDoxuL2V488o4vo6zbUUFHr4V7zna9R6JNu19vyhlrN5cQHxnCtR5cKstNjPTY2LXWPLGphEnJUZw7zbV2R+MxKTmakCDl0oaHiuZu3jlYwzeX5xIX4fvgJjwkiL/dtoTVU5LYW97CxbPTefcf1jDJhT8AhAj0Ol9GznxVAjlDvs4GqofeQWv9GPAYwJIlS7z+E712ofP1ggJ9W6sw3r+/c4T9lW08esviwebFP79yNh8cruOJzSUsn+T+Mtp4mS02Ht9UwspJSS43Bp6UbH+TLGnsZHq695bZKlu6WX+4lrvPnuzRBOycxEi2FXumR+Ke8lb2V7bxy6tnD3bB8KbQYBNTUmNcyrn748eFBJkUd63xfOHX8cpJjOTRW5b4ehgigAV6KpCRM187galKqQKlVChwA/Cmgc/vFll2FK7YUtTIs9vK+fZZBYOBF9j/6r92YRYbjtYbXitrqDf2VVHb3ss957jetHhw6avRuzNfz2wtQynFrSvzPHre3MRIusxWmrvMbp/ric0lxIYHc92i8Rd+ddUsF3Luypq6eHlPJTctzyUtVupmiYnD5IheAjXny7DgS2ttAb4PrAeOAi9prQ8b9fzuCvQoWxjHXq/oMDmJEfzooumn3f71pTlYbJr3DtX6YHT2Ho6PbSxmRnoM50xLcfnxMeEhJEeHUdrovTY93WYLL+wo55LZ6WR6uLGyp8pNVLX28P6hWm5cnktUmHGLCLMzY2no6KO+o3fM+/5hQyEhQYp7z3VtaVkIfxfo78mG1vnSWr+rtZ6mtZ6stf4PI5/bXYPry4F6pYVh1m4uobC+k59fMXvYhPSpqdFkxIX7LO/r0xP1nKzv5DvnTB73sltBciQlXgy+Xt1TRXuvhTu80H9woEG1u8HX01tKAbh1Zb6bI3LNrExHrbWq0We/Cus7eG1vJbesyCM1Rma9xMQS6KtRZ3SFe1dIzpdwRmNnHw9/dJILZqRy4Qj1ipRSLCtIZHtJs0+mzJ/YVEp6bDiXz8sY9znyk6IocaPH4Gi01jy5pZS5WXEszkvw+PlzEtyv9dXV55iZm5NOlodn5sYyLzuOkCDFtlGCd601//bWEaLCgvnOOTLrJSaeQN8EJ8GXkwbWlwP1QgtjPPJpET39Vn56+eilJJYXJNHQ0UepATsGhzpZ18GmwkZuWZlHSND4//sXpETR0NFHZ5/Fg6Oz+/xkI4X1ndyxOt8rNZ8iQoNIjQlza8fjq3sqae+1cKcHCr+6KjI0mCV5iXx2YuQd4R8drefzk43804XTSHKynI4QgSTQJ0Qk+HKS9HYUY6lr7+WZbWVcuzB7zLpZywrsMzo7S5uNGNqgtVtKCQ02ceMy9+o95SXai316ulI82Jdtk6PD3JqZG0t+UtS4gy+rzV74dX5OPItyXdsp6ilnT0vhWG0H9e2n53319lv55dtHmJYWzS0e3qwghL+QZcczRKD3kRLe96dPCrHaNP/oRLX4guRowkNMHK/tMGBkdm3d/by6p5JrFmSSGOVcZ4eRDCSte7rWV3FDJ58cb+DmFbmEBXuvgOvk1CgKGzrH9dj1h2spbuzi22cV+Kwa+8BGiXcP1px222/XH6e8uZuHrpzt1uymEP5MEu7PENLbUYymtq2XdTsquH5JzmBC92iCTIqpqTGcqDMu+Fq3s5zefhu3r/LfHolPbiklNMjETcu9O2MzOSWa5i6zy+UmtNb8+dNCCpKjuHSO92bmxjIzI4aFufE8vrkEi/WLEt/rD9fy+KYSbl2Zx6opyT4bnxDeFuhFViX4clKgR9kTQX1HL/et28uSf/+Irz+61dDAZSxPbC7BqjXfdWFL/7S0GMNmvixWG09vLWN5QeLgbjl3xEWGEBcR4tE2PW09/by8u5Ir52eSEuPdPKWBZeFiF2e/Pj/ZyKGqdu45exJBBhRVHYlSinvOnkRFcw+PbiwG4MMjdfzjur0syInnp37QvkoIb3Klt+O7B2t4dluZt4fkEgm+nBTo68uBrrKlm2v/tIV3D9Vy1tRkiuo7ueXx7XT09vt6aLT19PP89nIun5tBTuLYs14DpqdHU9/RR2u3+8U+x/LR0XqqWnu4w4MJ4rmJkZR5MPj6+64Kus1Wr5SXONWUVHvwVeRi8PXnTwtJiw3j2kWea3c0XhfNSueq+Zn8dv1xVv1qA99+ehfT0mL4221LfNo8WwgjuDIh8uqeKgm+AlWgb2sNZN1mC3c+uZOO3n5e+c4qfv+NBTxx+1LqO/r43YcnfD08nt1WRmefxeVq8VPT7K15TtSNL/fIFWs3l5AVH8FXRih/MR65iZEeW3a02uzlJZblJzIny/mG0eOVGR9BWLCJogbny2XsKW9hW3Ez3z5rklfz0ZxlMin++/r5/PSyGczPiedfr5jFS/esJFl2N4ozgCsTIg2dfV6fTXeVBF9OCvRtrYHsl28f5WR9J3+6aRFzs+1vzPNz4rl2QRYv76qkt9/qs7H19ltZu7mUs6elMDvTtaBh2mDw5d2lxyPV7Wwvaea2VXkeXSrLTYqksqUbqwfW4j88UkdlS48hs15gz7mbnBLNMReWff/8SRFxESFu7xT1pNBgE3efPZm/3LyYu9YUyIyXOGO4sgmusaOPFD/7o0SCLyfJsqNv7C5r5oUd5XxrTQFnTf1yK5xrFmbR0Wfh0+P1PhodvLKnksbOPr4zjh6JGbHhhAabPJo3NZwnt5QQERLEN5Z4NmjITYyk36qpaetx+1zemJkby7zsOA5UtjqVM7K/opWPjtZxx+p8Q1sJCSGGN/iePEb0pbWmobOPZJn5CkyScG88i9XGv75+mPTYcO67cNppt6+anERydChvHTh9u70RrDbNXzcWMz87jpWTklx+vMmkyEmIoMxLleIBmrvMvL6vmusWZREXGeLRc3uqR+Lh6rbBmblgA0sjzM+Jp7W736nx/3b9cRIiQ7hrjfFFVYUQp3O29mZHnwWzxSYzX4Eq0Le1BqLntpdzpKadf71i1rCzDcFBJs6amsL2Yt+06fnkWD2lTd18++xJ4673lOdGsU9nvLCjHLPFxu2r8j1+7sHgy83xP7m51Cszc2NZkGMvkLqvonXU+20pbGRTYSPfO28KMeGeDWCFEOPj7IRIY0cfAMkx7tU29DQJvpzkyrZW4b7OPgsPbzjJqslJXDY3fcT7LcqNp7Gzj8oW95e+XPXkllIy4sK5ePbI4xtLXlIk5c3dXvm96rfaeGZrGWumJA8m93tSRlw4wSbl1sxXY2cfb+yr5quLPT8zN5apqdFEhASxt3zk4Mtm0/z6/WNkxoVz8wqpFi+Evxho+TfWa2fDQPAlM1+BSZYdjfXUllKau8z8+OLpo84qLcy1t+nZU95i1NCAL3ok3rzCvR6JeYmRdJutNHZ6vtzE+4dqqW3v9VoSe3CQiayECLeCr+e2lWO2eqbwq6uCg0wszktg48mGEV/An9texv7KNn58yXRJZhfCjzi77Djw2iq7HQOUs8l9wn1tPf08+lkRF8xIHQyuRjIjPYbI0CD2lBkbfD3pqR6JSfYeieXNns/7enJLKXlJkZw3PdXj5x6Qmxg57uCrx2zlqa2lnDc9ZbDultEunpNOcUMXJ+tPL/dR197Lb94/zuopSVyzwPd1vYQQX3B2QqShw97/VGa+ApT0djTOE5tKaO+18E9fOT3J/lTBQSbmZMVxsKrNgJHZ2XskVnmmR6KjFVFpo2fzvg5UtrK7rIXbVuZj8mIldneCr7/vrqC5y8y9507x8Kicd/GsNJQ6vUei1poH3ziE2WrjP66Z67MejkKI4Tmbh93YaSbIpEiIlJyvgDTRejvWd/Ty6/eP8b3n9rDhaJ2vhzOoq8/C2s0lfGVWmtPFNqemRlNY32nYtXlpVwU9/VZu80ASe3ZCBErh0UrxAGs3lxIdFsz1S7I9et5T5SdF0drd73KPRIvVxmMbi1mUG8/S/NFnN70pNTacVZOTeGZr2Ze6JTy2sZj1h+v44VemkZ8c5bPxCSGG52ztzcbOPhKjQn3aDmw4z8IijgAAIABJREFUEnw5aWD2YCLMfB2rbefK/9vEXzcWs72kibue2sV7B31TruFU63ZW0N5r4V4XeiROSY2mvddCQ2efF0dmZ7VpntpayrKCRJeLqg4nLDiIzLgIyj1YbqK+vZe3D1TztcXZXt+dNy19fIVi3zlYQ2VLD/eeO8Xns0o/uWQGTV1mHnrzCO29/fxhw0l+9d4xLpubzt1nu16/TQjhfc6mAtX7YYFVkODLaROlyGp9Ry93rt2JQvHWD9aw5f4LmJ8Tz09eOUBbj2/7JPZbbTz+eTHLChJZNEau11BTU+0BQOEweTuetuGovRK7J0s3eLpH4nPby7HYtEdm5sYyfRxV+rXW/OXTIqamRnPBDO/lozlrXnY83z9vCq/sqWTeQx/wuw9PcMW8DP73Gwt9HhgKIYbnbM5XXXsv6XHhBozINRJ8OWki9HbUWvOTlw/Q3G3mb7ctYWZGLKHBJn5x1Wzaey2846NipQPePlBNdVuvy9XiB5K1jQi+BspLXOTBSuz5yZFu18oa0Gex8tz2Ms6bnkqBActlabFhxIYHc9yFNj2fnmjgWG0H95wz2av5aK7454un89Sdy/jxxdN57lvL+b8bFxIaLC+PQvgrZ3O+6tp7SYuVma+ANRF6O762t4pPjjdw/yUzvpRPNS87jmlp0by8u8JnY9Na8+hnxUxLi+bcaa7NhqTFhhEdFuz14Ot4bQdbipq4ZaVnK7HnJkbR1GWms8/i9rne3l9DY6fZsB6JSimmpcU4PfOlteYPG06SGRfOVfMzvTw615wzLYXvnTeF1VOSZcZLCD+nlEKp0fOw+602GjvNpMXKzFfAcmbZ0WbTPL+9nJ+/cYhjte0Gjcw53WYLv3n/OPOz47h1Zf6XblNKce3CbPaUt1Lb1uuT8Q3Ohpzt+myIUorJqdEUNXg3+HpySylhwSZuWOrZSux5jh2P7rYZ0lqzdksJU1KjWTMl2RNDc8q09BiO13Y4teHh42P17C1v5R8umCozS0IIt5iUGnXZsd5RYFWCrwA21vqy1poHXj3IT187yHPby7nxsW2UNnqvZ5+r/rqxhNr2Xn52xaxhg5vVU+y9CXeVNRs9NAD+9nkx6bHhXDnO2ZC8xEivtulp7Tbz2t5KrlmQ5XZ5iVN5qk3P7rIWDlW1c/uqfENnbuZkxtHea6F0jPHbbJr//uAEeUmRfHWxd3dhCiEmPpMafUKkrt0+mZAuwVfgGmt9+ZU9Vby4q4IfnD+Fj354Dl1mK09uKTVugKOob+/l0Y1FXDY3naX5icPeZ2ZGLBEhQewqNbZYKdirxW8utC/njXc2JC8pkurWHswWm4dHZ/fizgp6+21eSWIfmPkaK3gZy9rNpcSGB3PdImMLgi4rsP9O7ShpGvV+7x6q4WhNO/ddONWtrgBCCAH2VY/RZr7qHCs5qZLzFbhG6+3Y1t3Pv79zhCV5CfzThfa6QOdPT+WdgzVY/aA2xZ8/LcJssfGTS2aMeJ+QIBMLcuJ9MvP11Fb3q8XnJkZi01DV6vkej1ab5umtZSwvSGRWZqzHzx8THkJiVKhbVe6rW3t4/3AtNy7LJTL09Cbk3jQ5JYqkqFC2l4z8u9NjtvKrd48xIz2Gq+ZLtXghhPtMY+R8Dcx8ybJjABtt2fFvm4pp7e7nF1fPGVzSu2pBJg0dfWwfYzbA2+o7enlhRznXLcoabGUzkiX5CRyt6aDb7H7it7Pae+3V4q+a7161+IHvzd28qeF8dLSOqtYeryax57q5bPrEphIAbllpfPNnpRRL8xPZMUrw9cdPTlLV2sMvrp7jd8UOhRCByZ7zNUrw1dFHSJAi0c+q24MEX04bKeG+vbeftZtLuXxuxpdmRc6elgLAbh8s4w31+Ocl9FttTrVwmZkRi9WmKW4wLlft77sq6TZb3a6bNbB0506T55E8ubmUrPgILpzpufISp8pPGn/w1dbdzws7yrlyXgbZCZEeHplz1kxNprKlh0PDtHkqaujksY3FXLcwa3CJUggh3DVWwn1dWy8p0WF+U9JmKAm+nDRSb8fX9lTR2WfhO+d8uSJ7dFgwOYkRHHex8rcntXSZeWZbGVfOz3Sq5pOR9bLAnoD9zNZSFuclON1KaCSpMWGEh5g8Vi9rwLHadrYWe768xKlyk6KoaRtfztqz28voMlu5+2znuwJ42pXzMgkNNvH3XV8uV2K22PjRS/sJDwnigctm+mh0QoiJSI2RcF/V2kNmfISBI3KeBF9OGq63o9aaZ7aVMT87jrnZpwcP012of+QNz2wro9ts5btONi7OT4oiyKQMC74+O9FAaVO3R5LYlVIerxQP8NSWUsJDTNywNMej5z1VniNnrbLFtfH39ltZu7mUs6eleCUfzVlxkSFcMjud1/ZW0eho86S15udvHmZfRSu//uo8UmL8L+lVCBG4TEqNWnuzuq2HrAQJvgKaaZgK99tLmims7+SmFcPn2UxLi6G4octrO/BG02ex8sy2Ms6ZlsJ0R/+9sYQGm8hLijQs+HpySykpMWFcMjvdI+fLTYzy6MxXS5eZ1/ZWcc2CLOK9nDMwWOvLxeDx1T32YMfVrgDe8P3zp9BrsfGP6/ayt7yF+17cxws7yvnuuZO5bG6Gr4cnhJhgRis1YbVpalp7ZeYr0A0GX0PiqGe3lREbHsyV84avTTU9PQaLTVPcaEwwM9Tb+2to6OjjrjUFLj1uSko0hV4uVgpQ0tjFZycauGl5rseKbeYlRVLe3O1UsU9nPL+jnN5+G3esdu1nOB6TUhxLvnXO/+ytNs1fPy9mXnYcKycleWtoTpuWFsMvrprN9uJmrv3zFt4+UMMPvzKNH1883ddDE0JMQKMl3Dd09GGxabL8NPgydk96ADu1zldLl5n1h2u5ZUU+EaFBwz5mmqPp8PHaDmakG7ckpLXmic0lTE2N5qyprlU6n5IazcfH6um32rxai+npraWEBCm+udxz1eJzEyPp6bfS0NFHqptbi/utNp7ZWsaaKclOzxy6IzEqlPTYcI7UON8Z4b1DNZQ0dvHHb/pPA+gbluWyekoyByrbmJsVR26SbzYACCEmvtHqfFW12lcR/DX4kpkvJw3slhgIst87VEu/VfPVxSPXLMpxVC6vMbhlz46SZg5Xt3PnmgKX35Tzk6Ow2DTVXqiXNaCrz8LLuyq5bG4GqTGeq7+SO86lu+G8d6iW2vZew3okAszKjOVItXPBl9Wm+d+PTjI1NZpL5/jXkl5OYiSXz8uQwEsI4VWj1fmqarW/757ROV9KqeuVUoeVUjal1BIjntPTTi018db+aianRDErY+QZreiwYKLDgg3vl/j4phISIkO4dqHrxSxzHKUKKpq9F3y9uqeSjj6Lx6vF5yUO9Eh0P/h6YlMJ+UmRnDfdtSbf7piVEUthQye9/dYx7/v2gWoK6zu578JpUjdLCHFGMin1pVSgoapa7O9hZ3rO1yHgOmCjQc/ncUOLrNa197KtpIkr52eOObOUFhtGfYdxwVd5UzcfHq3jm8tzCQ8Zfjl0NDmJ9l/UChd33TlLa81TW8uYlx3Hwpx4j547OyESk4JyNwut7ilvYV9FK7evyje0PsysTHudtZNj5H1ZrDYe/ugkM9JjuHSOZzYrCCFEoBkt4b66tYe4iBCiw/wzu8qQ4EtrfVRrfdyI5/KWoTlf7xyoQWu4YoRE+6HSYsMNnfl6bnsZJqW4ZUX+uB6fERdBsElR4YVipQCbC5sorO/ktpWeb/4cGmwiIy7C7WXHtZtLiQkL5mtLvFte4lRzMu3lSvZVjF6Y98VdFRQ3dnHfhdP8snigEEIYYbScr4qWbrL9dMkR/CznSyl1t1Jql1JqV0NDg6+H8yVDezu+daCaWRmxg0VJR5MeG05de5+3hwfYy0v8fXclF85MJT1ufLlUQSZFZnwEFS3eWXZ8ckspSVGhXD7PO3lKeW5UigeoaevhvYM1fGNpjuF/MeUkRpCdEMHGk40j3qetu5//Xn+c5QWJXDzbexX3hRDC35lMI+d8lTd1D5bw8UceC76UUh8ppQ4N83G1s+fQWj+mtV6itV6SkpLiqaF5xEDwVdnaw97yVqeDh7S4cOo7erEZ0GB7/eE6mrvMfHO5e/39chIjvNKmp6K5mw3H6rhhWc64lkSdMVBuYrye2VqGTWuP56M5QynFWVNT2FrURL91+ESG3390graefh66arbf7HAUQghfGKnUhNWmqWjpJjdx7M4uvuKx4EtrfaHWes4wH2946jl8aWB156MjdQBOzzqkxYTRb9U0d5u9NbRBz20rIycxgrOmuFZe4lS5iZFUeiH4enabfUn05hGK0npCbmIUzV1mOnr7XX5sV5+F53eUc+HMtMGdqkY7e2oynX0W9pSdvvR4qKqNZ7aVcdPyPGaOstFDCCHOBCP1dqxu7aHfqs+Mma+JbmCWoaihi7ykSCanjL3kCAwu/9W1ezfvq7C+k+0lzdy4LNftPKDshEiausx09Vk8NDroMVtZt7OCi2enkRHnvXV4dxpsr9tZQWt3P/ec47seiWumJhMdFszzO8q/dLzHbOW+F/eRHB3Kjy6a5qPRCSGE/xipt+PA63+ej/6IdoZRpSauVUpVAiuBd5RS6414Xk8aGs9cMCPN6SWfgWKf3g6+XthRTrBJcf1i95PEB2Z9Kj2Y9/XGviraevq5bWW+x845nFzH2F1tM2S22Pjb58UsK0hkcV6CN4bmlJjwEG5YmsPbB2oGvweL1cZ9L+6lqKGT/7l+gddbHQkhRCAYqbfjQN6vP9caNGq342ta62ytdZjWOk1rfbERz+tJpiHB1oUzna/9lOYIvuq9mHTf22/llT2VXDw73SPNi3McO0Q8teNRa82TW0qZkR7DsoJEj5xzJOPtkfjGvipq2nq591zfzXoNuHNNAeHBJu56aidv7a/m1id2sP5wHQ9eMYs1LnYsEEKIiWqkUhNlzV2EBpm8usriLll2dNJA8BUTHsxSFwKIpCj7LEVTl/dyvt47VENrdz83eahVz8DMl6dqfW0vaeZYbQd3rPZ8eYlTxYSHkBgV6tKOR5tN88hnRczMiOXcab7f6JEZH8Ffb11CVWsPP3hhL/srWvnN1+YZ0mNSCCECxUgJ96WNXeQkRvh1AWr/rD7mhwZihnOmpbjU8zA8JIjI0CCavRh8PbetnILkKFZO9kxz5aSoUCJCgjxW5f7JzaUkRIZw9QLXK+6PR35SJEX1zjeo/vBoHUUNXfzhRv/pkbhqSjK7fnYhx2o7mJkeO2L/UCGEOFONVOerqKHL6bxsX5GZLyeFBZu4c3UBd589yeXHJkaF0uKl4OtEXQe7ylq4cVmOxwIHpZTHyk1UtnTzwZFablw2vor74zEnK47D1W1OlffQWvPnTwrJTYzkMj+rFh8ZGsyi3AQJvIQQYhjD9Xbst9oobexishN1OH1Jgi8nKaV48MpZzMt2vSVOYlSo15Ydn99eTmiQia95INF+qJyESCo9sOz4zLYylJfLS5xqTlYcXWYrxY1jtxn68Egd+yvb+O65kwl2YUZTCCGEbw1XaqK8uRuLTTNFZr5EYlSoV5Yde8z2RPtL56aTGOXZHXA5iZFUNHePWD3YGT1mK+t2VHDJ7HRDm5vOzbK36TlU1Tbq/aw2zX9/cJxJyVF8bXG2EUMTQgjhIcMl3Bc6Uk5k5kt4Lfh660A1Hb0WvrnMM4n2Q2UnRNBlttLS7Xqx0gGvO8pL3L4633MDc8LU1GjCgk0cHCP4enN/FSfqOvnhRdNk1ksIIQLMcDlfRQ2O4CvFf6vbgwRfhkjyUvD1/PZypqRGe6V8w0C9rPGWm9Ba8+TmUmZnxrLE4LpZwUEm5mbFsaOkecT7dJst/Pf6E8zKiOWyOd7pMymEEMJ7hsv5KqzrJC02jJjwEB+NyjkSfBkgMSqMnn4rPWarx855pLqdfRWt3Lgs1ys79NwtN7G1uInjdR3cvsr75SWGc96MVA5WtY1Y3Pbhj05S1drDz6+c5XZHACGEEMYbrtTEsdoOpqf7f/s1Cb4MkBhlj8CbujxXaPX5HWWEBpv46iLvlG8YDL7GWW7i8c9LSIwK5cr5mZ4cltMucBTC/fhY/Wm3Ha5u42+bSvjGkhyWT/JMeQ4hhBDGMimFzfbF1xarjcL6Tmamx/huUE6S4MsAiVH2qvOeWnrs6rPw+t5qrpiX4bVWM9FhwSREhoxr5utEXQcbjtVz28p8w8pLnGp6WgzZCRG8trfqS8d7+6385JUDJESG8MBlM3wyNiGEEO47tbdjSWMXZquN6RJ8CWBwJ6Knyk28ub+azj6Lxyraj2Rgx6OrHttYTERIELeuNK68xKmUUty1poAdJc1sKWwE7Lsb73/lAIeq2vnPa+dKj0QhhAhgp/Z2PFbbAcAMWXYU8EWLIU8VWn1+eznT02JYlOvdRPacBNeDr5q2Ht7YV8U3luaQ4OHyF666cVkumXHh3PfiPl7aWcHta3fw+r5qfnzxdC6a7V8FVYUQQrjGZPryzNex2naCTYrJqf690xEk+DLEQBDiiWXHg5VtHKxq45vLvZNoP1R2YgRVrT1YnagUP2Dt5lJsGu5a4/s+hOEhQay9YxnBJsW/vHKAfRWt/PLq2XzvvCm+HpoQQgg3nZpwf6iqnSmp0YQF+39XEOntaIDY8GBCgpRHlh2f31FGREgQ13op0X6oySnR9Fs1pU3O9clq6+nn+e3lXDEvYzBh39emp8fw8T+fS2VLN+lxEUSHya+8EEJMBEPrfGmtOVDZyldmpfl2UE6SmS8DKKVIiAyludO94Kujt5839lVz5fwMYg2oYTIrw75ufqS63an7P7utjM4+y7j6X3pTeEgQU1JjJPASQogJZGidr8qWHlq6+5mf43oLQF+Q4Msgnujv+Pq+arrNVr653JhE9qlp0QSbFEdrxg6+2nv7eWxjMedNT2F2ZpwBoxNCCHEmG9rbcV9FKwDzx9F/2Rck+DJIUnQoLd3jD7601jy3rYzZmbHMzzYmuAkLDmJKajRHnAi+nthUQltPPz/8ynQDRiaEEOJMN7S344HKVkKDTQFRZgIk+DJMQqR7LYb2lLdwrLaDm1fkGVoxflZm7JjLjq3dZh7/vISLZ6cx16DAUAghxJltaM7X/so2ZmfGEhIgfXoDY5QTQFJUKE2d469w/9y2cqLDgrnK4Irx87LiqO/oG7XkxJ8/LaLTbOGfvjLNwJEJIYQ4kw3kfFltmkNVbQGz5AgSfBkmMSqM9l4L/Vbb2Hc+RUuXmbcP1nDtwiyiDE4aP3taCgCfHj+9TQ/A8doOnthUwtcX5wREYTshhBATw0CpicL6TrrNVuYF0MqLBF8GSYx2FFodR97XK3sqMVts3LTCuxXth1OQHEVuYiSfnWg47TatNT97/SAx4cHcf6m06hFCCGGcgYT7/ZWOZPsA2ekIEnwZJjFyfIVWtdY8t72cJXkJPplZUkpx7vQUNhc20d7b/6XbXtxZwc7SFu6/dIbPq9kLIYQ4swz0dtxf0UpMWDAFSf5f2X6ABF8GGejv6Gqtry1FTZQ0dvlk1mvA15fk0NNv5cnNpYPHDlW18fM3D7NyUhLXL87x2diEEEKcmQZ6O+4oaWZRXgImk3Gb0dwlVScNkuRYdmx0cebrue1lxEeGcOmcDG8MyylzsuK4cGYqf91YzLKCRHr6rfzTi/tIjArlDzcuDKhfeCGEEBODSUFTZx/tvRZDur54ksx8GSQtNhyA2rYepx9T397LB4fruH5xNuEhvu1V9fMrZxMfFcINj23jjrU7SYgM5cW7V5ISE+bTcQkhhDgzmZSivdcCwPKCJB+PxjUy82WQuIgQYsKCqW7tdfoxz24rw6q1YRXtR5OTGMkb31vDh0dqCQsO4rK5GYQGS+wuhBDCNwZqXkaEBAXUTkeQ4MtQWQkRVLY4N/PV22/l2e3lXDAjlYJk/0giTIwK5RtLfZd7JoQQQgwYyHhZnJcQMMVVBwTWaANcZnwEVa3OBV+v762iucvMnWsKvDwqIYQQIvCYHDNfywsSfTwS10nwZaCs+AiqWkauFD9Aa80Tm0uYmRHLykmBtY4thBBCGMHkiGCWB+D7pARfBsqMj6C910LHKfWyTrWpsJETdZ3ctabA0D6OQgghRKAICTIRFmxifk5g5XuB5HwZKishAoDq1l6mp4eMeL/HN5WQHB3GlfN9V15CCCGE8Gd3rSngK7PSCAv2bTWA8ZCZLwNlxduDr6rWkZceT9R18OnxBm5dmReQv1BCCCGEEfKSojhraoqvhzEuhgRfSqnfKqWOKaUOKKVeU0oFTgMmD5rk2LV4oq5zxPs8vOEkUaFB3LzC9+UlhBBCCOF5Rs18fQjM0VrPA04ADxj0vH4lISqU3MRI9le0Dnv7sdp23jlQwx2rCwbbEQkhhBBiYjEk+NJaf6C1tji+3AZkG/G8/mhedhwHKtuGve3hj04SExbMt86S8hJCCCHEROWLnK87gfeGu0EpdbdSapdSaldDQ4PBwzLGgpx4qlp7aOjo+9LxA5WtvHeoljvWFBAfKbNeQgghxETlseBLKfWRUurQMB9XD7nP/wMswHPDnUNr/ZjWeonWeklKSmAm0Y1lfo493W13WfPgMZtN86+vHyIlJkxmvYQQQogJzmOlJrTWF452u1LqNuAK4AKttfbU8waa+dnxpMaE8cKOCi6ZYy8l8ZfPithf2cbDNywgNnzkEhRCCCGECHyG1PlSSl0C/AQ4R2s9don3CSw02MTNK/L43Ycn2F3WQkVzN7/78ARXzMvgqvmZvh6eEEIIIbzMqCKrfwTCgA8dFdu3aa2/Y9Bz+52blufywo5yvvqXLYC9L9Wvrpsr1eyFEEKIM4AhwZfWeooRzxMokqLDePsHa3hqSylZCRFcvSCL8BApqCqEEEKcCaS9kI8kRYfxw4um+3oYQgghhDCYtBcSQgghhDCQBF9CCCGEEAaS4EsIIYQQwkASfAkhhBBCGEiCLyGEEEIIA0nwJYQQQghhIAm+hBBCCCEMpPy1zaJSqgEoM+CpkoFGA55HeJ9cy4lDruXEItdz4pBrObI8rXWKM3f02+DLKEqpXVrrJb4eh3CfXMuJQ67lxCLXc+KQa+kZsuwohBBCCGEgCb6EEEIIIQwkwRc85usBCI+RazlxyLWcWOR6ThxyLT3gjM/5EkIIIYQwksx8CSGEEEIY6IwNvpRSlyiljiulCpVS9/t6POILSqknlFL1SqlDQ44lKqU+VEqddPyb4DiulFJ/cFzHA0qpRUMec5vj/ieVUrcNOb5YKXXQ8Zg/KKWUsd/hmUEplaOU+kQpdVQpdVgp9Y+O43ItA5BSKlwptUMptd9xPf/NcbxAKbXdcW1eVEqFOo6HOb4udNyeP+RcDziOH1dKXTzkuLwuG0gpFaSU2quUetvxtVxLo2itz7gPIAgoAiYBocB+YJavxyUfg9fnbGARcGjIsd8A9zs+vx/4tePzy4D3AAWsALY7jicCxY5/ExyfJzhu2wGsdDzmPeBSX3/PE/EDyAAWOT6PAU4As+RaBuaH42cc7fg8BNjuuE4vATc4jj8C3Ov4/LvAI47PbwBedHw+y/GaGwYUOF6Lg+R12SfX9IfA88Dbjq/lWhr0cabOfC0DCrXWxVprM7AOuNrHYxIOWuuNQPMph68GnnJ8/hRwzZDjT2u7bUC8UioDuBj4UGvdrLVuAT4ELnHcFqu13qrtrx5PDzmX8CCtdY3Weo/j8w7gKJCFXMuA5LgunY4vQxwfGjgfeNlx/NTrOXCdXwYucMxMXg2s01r3aa1LgELsr8nyumwgpVQ2cDnwN8fXCrmWhjlTg68soGLI15WOY8J/pWmta8D+pg6kOo6PdC1HO145zHHhRY5lioXYZ0vkWgYoxzLVPqAeexBcBLRqrS2Ouwy9BoPXzXF7G5CE69dZeMf/Av8C2BxfJyHX0jBnavA1XF6IbPsMTCNdS1ePCy9RSkUDrwD3aa3bR7vrMMfkWvoRrbVVa70AyMY+uzFzuLs5/pXr6aeUUlcA9Vrr3UMPD3NXuZZecqYGX5VAzpCvs4FqH41FOKfOscyE4996x/GRruVox7OHOS68QCkVgj3wek5r/arjsFzLAKe1bgU+xZ7zFa+UCnbcNPQaDF43x+1x2NMJXL3OwvNWA1cppUqxLwmej30mTK6lQc7U4GsnMNWxsyMUewLhmz4ekxjdm8DALrfbgDeGHL/VsVNuBdDmWMpaD1yklEpw7Ka7CFjvuK1DKbXCkbNw65BzCQ9y/HwfB45qrX835Ca5lgFIKZWilIp3fB4BXIg9j+8T4GuOu516PQeu89eAjx25eW8CNzh20BUAU7FvnJDXZYNorR/QWmdrrfOx/5w/1lrfhFxL4/g6499XH9h3Vp3AnrPw/3w9Hvn40rV5AagB+rH/BXUX9vyCDcBJx7+Jjvsq4E+O63gQWDLkPHdiTwAtBO4YcnwJcMjxmD/iKDYsHx6/jmuwLzUcAPY5Pi6TaxmYH8A8YK/jeh4CHnQcn4T9DbcQ+DsQ5jge7vi60HH7pCHn+n+Oa3acITtU5XXZJ9f1XL7Y7SjX0qAPqXAvhBBCCGGgM3XZUQghhBDCJyT4EkIIIYQwkARfQgghhBAGkuBLCCGEEMJAEnwJIYQQQhhIgi8hhBBCCANJ8CWEEEIIYSAJvoQQE5ZSqlQpdaGHz/lTpdTfPHlOIcSZRYIvIYThlFJrlFJblFJtSqlmpdRmpdRSN8/5pFLq3z01xpForf9Ta/0tbz+PEGLiCh77LkII4TlKqVjgbeBe4CUgFDgL6PPluIQQwigy8yWEMNo0AK31C1prq9a6R2v9AXDcMQs2d+COSqlUpVSPo6nzuUqpSqXUj5RS9UqpGqXUHY773Q3cBPyLUqpTKfXWkOdboJQ64Jhle1EpFT7k/FcopfYppVodM3Hzhtz2E6VUlVKqQyl1XCl1geP1EYIbAAAgAElEQVT4Q0qpZx2fhyulnlVKNTnOsVMplea4LU4p9bhjnFVKqX9XSgV578cqhAgUEnwJIYx2ArAqpZ5SSl2qlEoA0Fr3AeuAm4fc90bgI611g+PrdCAOyMLecP1PSqkErfVjwHPAb7TW0VrrK4ec4+vAJUAB9ubQtwMopRYBTwD3YG/2/SjwplIqTCk1Hfg+sFRrHQNcDJQO873c5hhPjuMc3wF6HLc9BViAKcBC4CJAliuFEBJ8CSGMpbVuB9YAGvgr0KCUetMxY/QU8E2l1MBr0y3AM0Me3g/8Qmvdr7V+F+gEpo/xlH/QWldrrZuBt4AFjuPfBh7VWm93zMA9hX3pcwVgBcKAWUqpEK11qda6aJhz92MPuqY4zrFba93u+F4uBe7TWndpreuB3wM3OP2DEkJMWBJ8CSEMp7U+qrW+XWudDcwBMoH/1VpvB7qAc5RSM7DPGr055KFNWmvLkK+7gegxnq52hPvnAT9yLBe2KqVasc9gZWqtC4H7gIeAeqXUOqVU5jDnfgZYD6xTSlUrpX6jlApxnDsEqBly7keB1DHGKoQ4A0jwJYTwKa31MeBJ7EEY2Ge/bsY+6/Wy1rrX2VO5+NQVwH9oreOHfERqrV9wjOt5rfUa7IGUBn49zNj7tdb/prWeBawCrgBudZy7D0gecu5YrfVsF8cohJiAJPgSQhhKKTXDkTSf7fg6B3tu1zbHXZ4BrsUegD3twqnrgEku3P+vwHeUUsuVXZRS6nKlVIxSarpS6nylVBjQiz2PyzrM93KeUmquI5G+HfsypFVrXQN8APyPUipWKWVSSk1WSp3jwviEEBOUBF9CCKN1AMuB7UqpLuxB1yHgRwBa60pgD/bZps9dOO/j2HO0WpVSr491Z631Lux5X38EWoBCHMn42PO9/gtoxL5smQr8dJjTpAMvYw+8jgKfAc86brsVexmNI47zvwxkuPD9CCEmKKW1qzP1QgjhXUqpJ4BqrfXPfD0WIYTwNCmyKoTwK0qpfOA67OUZhBBiwpFlRyGE31BK/RL7EuRvtdYlvh6PEEJ4gyw7CiGEEEIYSGa+hBBCCCEM5Lc5X8nJyTo/P9/XwxBCCCGEGNPu3bsbtdYpztzXb4Ov/Px8du3a5ethCCGEEEKMSSlV5ux9ZdlRCCGEEMJAEnwJIYQQQhhIgi8hhBBCCAN5JPhSSl2ilDqulCpUSt0/zO25SqlPlFJ7lVIHlFKXeeJ5hRBCCCECjdvBl6Oh7J+AS4FZwI1KqVmn3O1nwEta64XADcCf3X1eIYQQQohA5ImZr2VAoda6WGttBtYBV59yHw3EOj6PA6o98LxuK2nsot9q8/UwnBZIY9VaY7NJAV8hxOkC6bXBagus1zKzJXDeJyCw3tc8yRPBVxZQMeTrSsexoR4CblZKVQLvAj/wwPO6pa2nn+sf2cJdT+2iq8/i6+GM6aVdFcx+cD2/eu+o378QaK35ySsHWPzvH/LSzoqxH+BjXX0WLn34cy7+/Ua2FjX5ejhjOlrTzqpfbeDrj26lqrXH18MZ05v7qzn3t59w77O7sQTAC+2v3z/Gql9t4Lfrj/l6KGPqNlv4wQt7mfvQej46Uufr4YyprKmLrz+ylRW/2kBFc7evhzOmHSXNnPXrj7n58e309lt9PZwxvby7kjkPredX7wbG+8SDbxxiwb99wCu7K309HMN5IvhSwxw79arfCDyptc4GLgOeUUqd9txKqbuVUruUUrsaGho8MLSRxUWE8M8XTWfTyQZ+/b5/v8geqmrj/lcOkBITxqOfFfPOwRpfD2lUL+6s4KVdlUSGBvPAawep9vMA4T/ePcqx2nbaevr56WsHsfrxi5bVprn/1YP09FvZX9HK/6w/7ushjaqly8zPXjtIn8XGe4dqecHPg/HdZc385dMiAP78aRH7Klp9PKLRPbO1jLf2VxMTFsy/vHKAxs4+Xw9pVL98+yhHa9rp6bfy3ef24M/t7cwWG999bjca2FrcxC/fPuLrIY3qWG07//z3/aREh/HoxmJe31fl6yGNat3OCp7eWkZ8ZCj//PJ+ypq6fD0kQ3ki+KoEcoZ8nc3py4p3AS8BaK23AuFA8qkn0lo/prVeorVekpLiVJFYt9ywLJer5mfy2t4qv/6r5uXdlQQHmXjnH9aQkxjBc9udruPmE89uL2NuVhwv3rMCgKe3+u9423r6eWlnBTcvz+PBK2dR0tjFe4f8N7jdVNjI/opWfnb5LG5dmcfr+6oobfTfF621W0rp7LOw9o6lLCtI5OGPTvp1cPvwhkKSo0N5/XurSYoK448fF/p6SCPqs1h5fFMJq6ck8cQdS2nuMvPaHv99wy1r6mLDsTruWJ3PTy+bycGqNvZXtvl6WCNaf7iWxk4zv7puLl9dlM0b+6r9+n3ipZ2VhAaZeOsHayhIjuJFP/9DZ92OcmZmxPLKvaswKcULO/x7vJ7mieBrJzBVKVWglArFnlD/5in3KQcuAFBKzcQefHl3astJ1y/JoaPXwgd+OmVvsdp4+0A1F8xIJT4ylBuX5bKtuNlv33DLmro4VNXO1QsyyU6I5KJZaby0q8Jvp8A/OVaPxaa5dlEWF89OJys+gjf2+UVK4rA+OlJHREgQl8/L4I7VBdg0fOinv7tgH++S/ERmpMdy0/JcGjv7OFDpn7NJ7b39bC5s5BtLc0iNDefSOelsLmz02zfcrUVN1Hf0cefqAmakxzIzI5b1h2t9PawRvby7EpNS3Lwij8vmZhASpHjXj2fxX9xZQXZCBGdPTeHahVl09lnYcLTe18Maltli4/V9VVw4K5XEqFC+tjib7SXNlDf559JuSWMX+yvbuHZhJulx4Zw/I5WXd1f49R9mnuZ28KW1tgDfB9YDR7HvajyslPqFUuoqx91+BHxbKbUfeAG4XfvJfPPKSUkkR4ex4ah/voHtLG2hsdPM1QsyAbhsTgZgnwHxR+8etL/4XzrXPs4LZqbR3GXmRH2HL4c1ovWHa0mNCWNBdjxBJsVZU5PZVtzkly8CWms+PlbPmqnJhIcEkRkfwZTUaD7309+F+vZejtS0c+50+yz22VNTMCn49Lhf/N11mq1F9ut+9lT7eC+YmUpPv9Vv8wC3FjUREqRYNdm+iHDRrDR2l7fQ0OGfS49bi5qYlx1Hamw4cREhrJmSzDsHavxy6bG338qOkmYunZOOyaRYMSmJlJgwv50V31/ZSnOXmavm298nBv79+Jh/vq+9f8j+PnGlY5yXz82gsdPM0Zp2Xw7LUB6p86W1fldrPU1rPVlr/R+OYw9qrd90fH5Ea71aaz1fa71Aa/2BJ57XE0wmxdL8BHaXtfh6KMPaU24f18pJ9hfYvKRIUmLC2Fna7MthjWhHSRPT0qLJio8AYHlBIgDbi/1vvDabZlNhI+fPSMVksqcurpqSTEevhcPV/rcccrK+k6rWHi6YkTp47KypyWwvbvLL2ZlPT9iDrHOn2cebEBXK/Jz4weP+5vOTDUSFBrEwNwGAFZOSiAwN4pPj/jnbsaWoiYW5CUSEBgFw4cw0tIYtRf4XjPeYreyvbGV5QdLgsXOnp1LV2kNNW68PRza8A5VtmK02lubbX7+CTIrlBYns8dP3iV2l9nENjDcnMZKMuHB2l/vnLPPushYmpUSREWd/n1jqeJ/w1/c1b5AK98DivAQqW3qoa/e/F4E9ZS1MTokiLjIEAKUUy/IT2Vnif7+kWmv2VbSyICd+8FhOYiRZ8RFsK/a/2YOSpi46ei0szP1ivCsn2d8cNhf633j3OV5IB16owB589Vls7PXDF9ldpc0kRoUyMyNm8NiaKckcrGylx+x/weLWoiaWT0oiNNj+shgeEsS87Dj2+2HSfVt3P4eq21g1+YtgZkZGDGHBJvZX+N8fDnvKW+i3apZP+uJ3d+B1wh83NQwEAQPBDMCi3ASq23qp9cNgcXdZM5OSo0iKDhs8tjgvgd1+GMxordlb3sLCnITBY1nxEWTFR0jwdaZZnGf/JfC32S+tNXsrWgf/Eh+wNN/+IlDZ8v/Ze7MYybL0vu93Yl9zidxqr+qlumd6Fs7SHEoWRMgmByABg8MHSSZhwyND0jwIhGHJEjCGDcKgIIAWLcgP4oPHNGDKgkBTgiwO7DHI4Vi2IUEUp8khZ6a7p7u6q6u69oyMyMzY9+OHGyciKisiM+69Z7lZFX+g0ZWZURFf3TznfP/v/y0nWvn8e9U2h60+n7v6tL0/8VKJ796J1rMFJrVHn70yJV87xTQvbecj6XB/8OCYQjrBS1v5yfeU7VFU6n74oManLq0hxLQh+lOX1hlJrzMrSmh2B9w+aD4VOAB85vI67z6uR24W0fcfHCHl0+QgGY/xqUtrkayp++6dKjEBb16fng2fvLhGKh6L5F77w4+q3NwtsJlPTb6ngrTvfRyts0xKyR/dPeQL158+d7943fMTUes2v1dtU2n2+ML1p/faj9/Y5A8/OoxkGtoEVuQLzyGkErHIbaq7lRbVZo8vnCBfnxt//cMH0XJg37vnPb8fu7r+1PffuLTGQaMbuTb4798/JpOMcXO38NT3P3mxGDlyAB75euPS2iRFCrBdSLNbTPNOxGoleoMRt/brfOrS02vhU5e8WctvP4yWvT96XEdKjxDM4tOX1+kNRrz/JFo1iz965Nlz0t7PXtng7Ye1yM1Te/dRjRtbeYqZ5OR7qUSMNy6t8b0Ikq+3Hx4/Q8SVn/jjCPqJw1Z/IiIoqK+jpoqr5/f5E0H6565ucNDoRrZmUTdW5AvvEHh1p8B7TxquTXkKqvjwM5efdmCv7XlkIWoO4QdjMvP6XvGp73/igucg3nscLXu/f/+YT19aJxF/eht84sIad6utSA3fHQxHvPuo9sxaAI/cvhMxMvP+kzr9oeTTl58mB1c2s6xnk5EjX4q8vnHpaXvV8/7hg2gpi+8+qrG3lqY0o8yAF/i0+0M+KEfrLHvvcZ3XLxSf+f7nrm7wwwfHkeqG9gLF3jP2phIxPnmhyLuPonWOvTf2A584Ye9re0ViInp+4t1HNVKJ2MSPKbyu/ETE7DWFFfka47W9Arci9ku/td9ACHj1hDKTSyW4VspFbpHe2m/wyk7hWTIzrvn5UYTIl5SSHz2qTZSYWXzy4hpSRusQ+LDcpDsYzSdfF9f4YL9BdxCdOiqVBj2pfAkh+NSltcilSd95WGM9m+TSeuap79/YylNMJyKnMr/7uD4JamahnvePIkQQWr0Bd6utufa+tlek1Rvy8Dg6qTFFVuaRxVd3i9yKWOe28ls3TwS9mWSca6Vc9Ozdb/Dydv4ZP6HIWNSCdFNYka8xbu4VeXTcod7puzZlgg/2G1zeyE66mWbx2l6R9yO2SD/YbzxDFMFLjW0XUrwXoVTefr1Lszeca6+KIKPU9vzBvqdk3Nx71t43Lq0xGEluRUi5/dHjOrlUnOul3DM/e+PiGu89rkdK7XjnUY03Lj5dnwZeN/QruwU+jJCS1BuM+GC//kzKEbxu6HhMcDtC9t560kDKRWTGW89qfUcB6lw9qeCDt/+e1LrUIuQnbo39RCGdeOZnN/eKvB+hcwHg1n79GaIIsDX2E1FT6kxhRb7GeG28GG5F6BC4td94ph5J4fULBT46aEbmEtVWb8CDozav7Cyytxgp5evD8e/55Tn2XtnMUkwnIhWBKWf60nb+mZ/d3PXWbpQIwkcHTV7azj9Vn6bw8k6B7mDEo4h0F0spub3fmEtsAV7eyXO7HJ2hxncqTfpD+UyaCSCdiHN1M8uHEbJX1U/OszeS5Gu/wUYuyU4x/czPXt2JoL1PFq/dm7sF7kTIT7R7Q+4ftifP8SRe2ytGrvzHFFbkawwleUYl9TgcST4sz1eSwFukg5Hko4hMulfOaZG9N3eLfLjfiEwniyIq88iiEIIb23nuRGg69O2DJpfWM+RSz0a317c8denOQXTsvTMmX/Ogvh+VWxoqzR717oAbW/PtfWWnwONaJzI1gGrPv7yz2N4oEfEPy01SiRjX5qigpXyKUj4VKXvff1zntd3iMyooTJXnDyJCEJSfeG2OkgRTP3EnIvcmflj2VNBFZPG1vSK3ntQj4ydMYkW+xri6mSOdiEUmorl/2KI3GE1UjZN4edtbvFEhX+q5LSJfN7ZyNHtDDho9m2YtxIflJvlUnL21Z6NbwCNfEXm24JGveSodeLUdl9YzfHQQjbXbG4y4d9jm5QXkS5GG2xF5vmoPLSKL6t8Rlb2m1uX1RWRxt8Dtg2Zkbmm4c9Dkeik3VwUFeGUnH5lzFzxlcRGxvaL8RETI4r2q5ycWnbtRUxYn5RML7H15J0+rN2T/Beh4XJGvMWIxwbVSjrsRUTuUY3ppwSFwbax2fFyNhkP4sNwgJqYqzEkoRxEle1/ZLcyNbsEji4oAu4aUktvlxkJyAN46+Sgia/feYYvhSC5cu7vFNLlUnI8ikho7i3y9FDGyeKfSopRPsZ5Nzv35Kzt5eoNRZOY7fVxtLTwXwCMIUSEHje6Ag0Zvcr6eRDwmeGk7H5mauo+r3p5fpNqq5x4lvybE4sBBqaNRsdckVuRrBtdKuclido17YzvmFSwDrGeTbOSSkVmkdystLm1kSSeebQ6A6KXGbpcXp8XAOxxGEh5EwIEdNHrUO4OF0Th4h29UlDpFqhY5BCEEN7bykVHq7hw0ScQEVzazc39+YyuPEETG4d6tNE8lM0ohjUIqT0rJ3UprobMFb68dtvqRaHZSF1FfLy2292opx72q+3MB4O7YT8xL6QIUM0lK+VSk/Nql9ezkFomTUOvkbkTSpCaxIl8z8DZVKxL55nvVFulEbG7Rp8L1KJHFwxZXNxc7hCubOWJieli4RH844tFxe+GBBZ7yBdGoS1IH0Y3TlK/tPMftPodN92nds5Qk8NSk6ChJTa6Wcs+0vit4ad1sJNYCeGtyEbEFJvvw3qF7glCud2n3h6eSxYm9ESA0Spk/y957h9HxE6lEjN1T/ITya1HAvWprYZAD3jVDMUFk/JpJrMjXDK6VvLqkagQc2MfVFldLuYVpMfA2VVSUr3vVNldLizdVKhHj0kY2EhHN4+MOI8mpZFERnSgUqt4fO9FT7R07448iYO/H1dZYmU0tfM31Uo4Hh+1I1CXdOWhNyPYiXNnMRkIF7fSHPDzunEq+dotpUvFYJK4fU00rpylf6ty4FwF71Xl69ZTA7FopS6s3pBIFP1FpcXUzu7CeDqIVpH9cbZ0a9E79RDTsNQkt5EsI8TNCiPeEEB8IIb6+4DV/WQjxjhDibSHEP9XxuboxyTdHYKF+XD1dmQEvOntw1HZ+71y7N+Sg0T2VHIBnbxQ6CFUUeFoEtpVPUUgnInEIKCd6mr3KWdyPgNpx/7DF5Y3FtoKnhA5GMhKX2d87bJ3qbMGzNyrPFk5XZmIxweXNLPcjoCSp4GVR+QTMKl/u99rdaouNXHJhPR1M91oUCM1ZZAY8vxYFP9Hpe4X0Z+2161u5SPhg0whNvoQQceDXgZ8F3gB+UQjxxonX3AT+K+DPSSk/BfwXYT/XBFSRpetDQErJ/SU21fVSnuFIOi+sfXB0drQIcK2Ud/5sYUZJOsVeIQSXN6Khdtw/bLNdSJNJzq+nA7i04U1md70WwKuTO40oAlwe/9z18611+tQ7gyXIYpbHtY7zBgy1ds96vlc2s5FQvu5XW8TE9Pc9Dxu5JIV0IhLk9l61dSpRhGmQ7vosk1Jyb0nyNRxJHh25DXTUejzb3jwfR0DBNw0dyteXgA+klLellD3gt4CvnHjNXwd+XUp5CCCl3NfwudqhIjDXasdRq0+9Ozj7gB3L9Q8cH1qqVuO0tCPA5Y0M1WaPTt/tNTj3Dj2HcOHEVTIncWkjEwkyc/+wfarzAq+wdi2TcL4WpJQ8WMJeRXZc26t+v5fOIF+XN7NICY8cX4PzcOxAz7L3ymYuEjVfD4467K1lSC6opwMv0IkMWTxsc2UJFRTcky/lJ84MelXHo+NOc6UUnuUnrpayHLb6kZmrZwo6yNdl4N7M1/fH35vFa8BrQoh/I4T4AyHEz8x7IyHE14QQbwkh3iqXyxpM84dsKs52IeXc4arah7M21cSBRcXeM9KOymG4fr73D9tcXM+e6hDAc7iubYXllCSAy5s552vhqNWn2RsupSQBzh2uIn9nkUVlbxTIYjwm2Fs7PXC4spml2uw5d2APj9pnEkWIRgehlF4W4ay1m03F2Smmndur9vqVM87dyxE5dydB+pL2ug50TEMH+ZpX6XeyijYB3AT+AvCLwG8IITae+UtSfkNK+aaU8s2dnR0NpvnHxfUsD4/dyrNqk5x1CCjl5pFje+8fts/szIRZ8uXW3rM6bhQubXgRWKvnzoGNRp6StBT52nBPFqcO4XR7M0kv0HFNFtXzunLGXlMOw3Vq7MFRmwtrGeKnFFhDdGoAHx4vR76ubGaddxBWmz26gxEXz1DEwTsbXF8GPlVtT7f3wnoGIdyfuw+P2qTiMbYLp/uJi+vR8BOmoYN83Qeuznx9BXg45zW/I6XsSyk/At7DI2ORw8X1DI8cOwRFps46BNKJONuFtHOHq6Lb0zozIToR2IOjs9NiEA17y40uveHozOgWxh15jp3ttCbpbHsvb2Sdk4P7SzqEC+sZYiICSt0SygzMquLu7B2N64zOIgfg2dvqDal13AU6y6Z0AS6uZZwHvVM/cbq9yXiMnULauZL06LjD3nr61M5MmJJJ1/aahg7y9V3gphDiJSFECvgF4JsnXvMvgX8fQAixjZeGvK3hs7Xj0kY2EpsqnYhRyi9u1Ve4tJFxrtQ9Pu5w4Yw0CMDemheBuVQ7hiPJfr3LpTMOLJh1YO6eryInl5d0YPXugOO2u2GVipwsQxCubOack8UHh20ubmTOdAjJeIy9tQz3IxDoLBM4TB2Yu7V70PQCh2XWglLxHzu0VylZy5wNFze8IN2lUvfw2AsctpbwExcj4dfaZxJFmPUTK+XrVEgpB8AvAb8LvAv8tpTybSHErwghfm78st8FKkKId4B/BfwdKWUl7GebwMX1DI3ugJrDacsPj9pcXM+cqSSBd1C4VpIeHXeWkurVMECX9h40ugxHkr0lUwvgts5HjWK4sLZMzZd7ex8fd8gkY2zkFrfqK3iBg1sHtqySBB5BcDkaYziSPD5eTknaKaSJCXjikswoJWkZMrPuXu1YNo0H3r+p6Vipe3TU8RTZMwIHgEvr7puHHh13uLTEuZuMx9grus9AmYaWOV9Sym9JKV+TUr4ipfx74+/9spTym+M/Synl35JSviGl/IyU8rd0fK4JXFTFfg5Z9+PjzpmdeAquI7DheFbTsva6rpWYSPVLKHW7xTTxmHCaulH2LvN81WtcEoQn9e44cj3bIeytZej0R9Ta7hzYEx977YLjVNN+vcNgJJdKiyXiXg2mS3uX7SQFuLCuiqzd2esn4xAFpc5Tkpb0E+ue8uXKT4wmfmK5QOfihvu0rmmsJtyfgGLmrgnCMtEizERgjhxYpdFlMJJLHwKeUueS2Hq/12UcbiLuKXVPal3TZi3Ek1qHVCLG5hJKkuqAc0q+ah32ikuSGeXAHNk7Gqegz+ocVLiwnnGqJD1eshZU4cJ61tmzBX9K0m4xjRBuydcDPxmHDfd+4uFRZyliC569LYd+4qDZpT+US60FiEZGxzRW5OsElPLlKqIZjiSPax0uLrtIVVG4o0Ng2aJPhb01t6mbZZsZFHaLafbr7siXqqdbxiHsjIvGXdpbrnfZXTu9eF1B1Qm6IgiHrR6DkTz1XrxZXFjL0OwNnV0ArX6vu0uSW9dF4U9qnpJ02rR4heQ40HnsMug9Wq4mCabnnasMico4+FG+wKGfOPLnJ6JQkmAaK/J1AntFr1bCVb5Z1SQtK8/urbl1uH7SYgC7a2lavSENR/OHHtc6pOLLpRYAdooZ9h2SRT8p6NQ4ZbJfd2OvlJ5DWJYcKMXJlcNVe8aP8gXuArMp+VqSLDpW6vbHRHyZwAE8pc5tWre7/Dk29hOu1u6ByjgsqXxddNxB6DfoVSUJ9ed40OqKfJ1AIh5jq+BO7fBTkwTTKNgVQVCb2Y+SBJ5C4gKKzCzrEHbX0s5sBY8sLtNJquAyTdroDmj1hpOA4CxMyZcbe5UC60f5AndKXbnWISZg64yxGAoX1zPUuwNnSl253l2aiINbpU5KLwW97FrwShLcdZrvj/f43pL2qr227+hs8FPuAUxmRrqy1wZW5GsOdgruHK4iUctG45NF6pDM+FGS3JPF5ZUk8BxzpdlzcimtlOMUtA97dxymSf0qSamE1ybvisz4TuM5Lgrfr3fZKqTPHLCq4LoBww+ZAc9eV6pirT2gNxidOSh6Fi4Ds3LDe07L2rtd8M5nZ36t3iURE5Ryy2YclF97fovuV+RrDlw6sHKjO7FhGWRTcYrphLtDoN5lp7h8amHXcZr0iU8lSREJF8/3sNWnNxgtTWbAs9cVsfWrJIHbGkD1nJatUVOvc5XKe1LrLK0qwlSpc0YWax1fa2F3LU2jO6Dds3/3q18yA66DdH9+Ip2Is55NuvNr9S7bhbMHrCqogMhl1sE0VuRrDnaLDiOaehchYKuwXIQAsOM0Auv6PrDAHflSZHFZ7DpUFh/7rKeD6dodjewXqiqHsOuDLLpUO/brXdYyCTLJ+FKvzyTjbOaSPHKqJPlTQcGrD7KNTt+bgRXkbHBh72Tt+ny+ZQe2wpSU+D3Lzo2fcFyeYgMr8jUHO8U0Bw03Dqxc71LKpc689HkWO4W0M3nWL5nZyCVJxWNO7G2Oa5L8HVju0qTqYPerJA1GkmqrZ8qshVC/Uz/qjEvly1OSlne24K2HA4epGz9rwaUDK/tM6YLbEor9gGSmMm6Qso1yo8t6Nkk6sVzgAG7J4n7N39pdyyRIJ2JOO7dNY0W+5mC3mGYwkhw6cWD+yAx4SoOrCOHAZ0QjhO3SQEwAACAASURBVPAOAQeFlJNoccmCZXCbJlVO/qx7B2cxUeocPN8ntS7ZZJxCOrH039kppqm2egwc1NSpbjw/2C6mnCgzw5Gk0vDnwArpBJlkzMnZoIj4jo/nGwmy6NPekYRK041S52ctgBqb4yhID+AndtfSTjvNTWNFvuZgR6kdjg4B3+TLUY3aYDii0uz5IjPgrqbObz0dwFY+hRCO1kIAe6dk0f6hpWqSlq3/A9gppJASN0pdzV8aD8Z1Pg7IV6XRZSRhx4dSNwl0XJCvmn/VdkK+XKQd6961WEWfgQM4Ios+yQwwWQu2Z2epwMG3vY72mi2syNccKAfmKgILQmZavSFNyzNRqs0eUvojB+AuAgtSJ5GIx9jKpyk7sjeXipP34RCmaVI3qRs/9V7gzoFJKX0NhFVw5cD8zvhScOXA/HaSAmzlvdlZzs5dH41D4JZ87df9NTOA97twMTur2ux5gUMAe1ejJl4wKPLjxCEEiBBcFYUHqZMAdy3aKl3kJ40H7mZnHTS6vm112aLtt7sNpr+Lg4Zd5euo1ac3HPlWvrYLaTr9EU3LHXlBOknBs/egbl9VLNe7xGOCrSVH0ADEY4JS3pFS57OZAWCn4KYjTwUOQZQvsG9vkHIPcDt1wAZW5GsOXBV+1jr+Z82Au6LwIGkx8OxVYxRsolzvEhMsPZNMYW/NnVLn99lmknE2cknrZNGbbr/8PYkK244CnScBmgPAnQPzO0NNwVWR9X69w3YhtfRoAQVnaVKfzQzgLk3a6A7o9P37CXdr199IF4XdYprjdp/uwP7oERvQQr6EED8jhHhPCPGBEOLrp7zuLwohpBDiTR2fawr5dIJ8Ku4uQjgnh0DQiGbXob1+hlQquJK/PeXLH1EEN2ndendAu7/8dHsFV+MQgowWgFmlzo29QZTQqoMhwUGUJHBHFoMEOq5mLAZJ6XqvdyMqTP2ET3sdlv/YQGjyJYSIA78O/CzwBvCLQog35ryuCPznwL8L+5k2sOPAgU06hIKmHS0ThKBkcVIUblupC1BPB569Bw5ayoM4BPAOZdvKV1Ayk08nyCbj1sc3PKmdN+WrQymfIpXwd2QreyuW07pBuvHAC+Rsr4VOf8hxux/MXgepsdBBum17VblH0V8g6fr2FtPQoXx9CfhASnlbStkDfgv4ypzX/V3g7wPnond0t2h/fMN0No6/TbWRS5KMCyeHQNHHkEqFXUfdpEHq6cD7fdhuKe8PRxy2+r6jRXBTU+d3WvwsXKgdQdUDl2nHoGQGHNkbdC1YbmgIMpNMYdtBmjRo88V61s2MxXK9SyGdIJdavnEInv8p9zrI12Xg3szX98ffm0AI8XngqpTy/zjtjYQQXxNCvCWEeKtcLmswLThc1B4ElWeFEE6uughKZlxFNAd1/wXsMDN6xKKapJQKv9EijNOk9Y5VBzatoQrgwAr2Z2eV612K6QTZlL/AYTOXIiYcpB0DqqDbDtK63giaYCrzTjFNbzii1rbXkRe0dlX9HdtKXVDly9XokaBrd6V8nY15BTSTU18IEQP+IfBfnvVGUspvSCnflFK+ubOzo8G04HBCvhpdUokYa1l/EQJ4839cRDRBDlg1O6tsMe0YtJMU3MzOClpPB14qrT+UHLb6us1aiCBznRS2HQQOT2qdQMpMPCbYcmCv10kaoIbKgfJVUSNoAhDxaf2qvb3m957EWbi4sqdc75KKx1jPJn3/XVeiQpBn68JP2IQO8nUfuDrz9RXg4czXReDTwP8jhLgD/Bngm1Evut8ppr0iYost5YrM+Jk1o+DiEDgIuKnU7CybEc1xu09/KAPZq9Qcm8qXcj7bgRyCZ6/Na3sOGl3SiZiv6fYK3nVelmuSAhaEg32yOBp5owX81qeBm2acMETcxd2v5YDdeODGT+zXO75nkim4IF9h/cTzOmhVB/n6LnBTCPGSECIF/ALwTfVDKeWxlHJbSnlDSnkD+APg56SUb2n4bGNwUdsRNEKA8xXRgH2yGFSqBzcOQc1mCpq6AbtF1pVmj+2AgcN2wX5H3kGjG4jYwvTuV1s4bPUYjGQgMpNJxilm7HbkqcAhaAE72D93Y8Ib8uoXLpTFcj3c2nXiJwKcYzBuaHhOB62GJl9SygHwS8DvAu8Cvy2lfFsI8StCiJ8L+/6uMG3LtZtqCkNmKhYdWLs3pN4dBLd3za7yFSaNl0rE2MglLTuw4GRxazyewmaDQLXZ8z0/TUH9G6tNi2Sx0fM1AHQWtusrDyb1f+fD4U6UrzBpR5v2BhxBA27SpOWAzRdwDv3EczxoVcucLynlt6SUr0kpX5FS/r3x935ZSvnNOa/9C1FXveB8Kl9gT+1QkX/giMayA5uSmWAOdyufskoOVEG4305SgO28/anxlUZw8mV70GqnP6TRHQSaoQbqcu2etYYGRaKDKDNgP02qPivI813LJEglYlZTTWGVGfUetnCe/ESYjAO4KaexhdWE+wWYtLlaOgT6wxHVVi9ERKPGN9iJwIJeLaSwNU412XJgQTtJFbbydlNNQZsDANayCRIxQcWivdVmCCXJcl2SItGlgGRmp2C3I085yq2AZNF2mrTS7FFMJ0gn/AcOLjq3w+w12+MQdPkJW/aGSUHDdAzNyPKMRRtYka8FKOW9lnJb+eagl1QrKNWhYkmdCRvRbBdS9Ib2LnktN7wOoSCdpOA5PtvKV5CxGOA5sFI+Zbnmqxs87aimxltyCOr3GIbMgL1U08Tec5ImrTZ7gZ8t2E+TVhrB7VV+wpa9yk8EPRts3/0a1k+U8imGI0mtY69z2xZW5GsB4jHBZi5lncwE3VRK4q/akpND1CTBDFm0KH8H7RACz1HbWgvgpXWDPlvwlEVb9rZ63l1zpRBpPLCnfFU0kBmAsqULqyvNHkLARi44WbTZkReGiIMD8tXsBl4LavSIrbokpWAGTZlvuQrSA/u1cZrU4tlrCyvydQpK+RRVS0XLYTfVVPmyJCfXuwgBpYAOYaugiqzt2Ru0YBm8FNVhq2ftiqEwdR3grSNba2GSFgvowHIp7y7VA1tkZrzXwjYIWCOLjS6buVSggnCwf3+mV/8XfO3aJF+TwCGEvVt5e4FZ2JS5WvO2VHxVd7oZcK/ZDtJtYkW+TkHJYpF12E1VSHuFqrYOAeUQEvFgS0g5altF4V5RbfBofLuQQkqv7d80Ov0h9U7wgnAYOwRLzzbs2oXxNS2Wa762QkbjNlNNoZQky6NSwtT/gbd2D1s9K3U+YQMHcOUnggY6cdKJmFV717NJkkH9hMroWOzctoUV+ToFNlNNYTeVEMK6ww3jEKabyl7qJmi3GEw7zWw834OQKV0Ypx2tk5lwBMFWzVel2SMZF6xlgtX/ec5EWCNflbBkRo0esbAepJSha75K+RQjCUdt83U+Yc9d9XetnWMhyaILPxFm7apAx/YQZhtYka9TYHVThXQIYLcovBKSfE3lZDsO4bDZC1yTBHbtnR6wYdKkKZq9IZ2++TqfsDVUMB6HYDGNV8qnAtf/xWKqocGevWHJDNgJdGrtAYOR1HI22FA7dAQOWxbXQrXZIx4Tga4WUigV7JXThK3/28zZDdJtYkW+TsFWPs1Rq8/AwkC6aqPHZi64QwAv7WPrEDgMGdGkE3GK6YSViKbW8RxCOHJgr1B1Eo2HTJOCLXvD1VCBmp1lM40XnNjCtAbQBkKrzHl7RcuTmWShyIx9lTlcoJOm1hlYGVxaaXp+Ihaw/g+8f6vNtGOYtZtKxFjLJKyOzbGFFfk6BeoAsXFBcVglCWDbcuFnWHttKXU6UguqPsiK8qVBSZo6MDv2puLB7nVUsBnoHDR6oerpwF6R9WA44qjdD0UOsqk42WScQ6t7LZxqO/teJqEj0FF/187zDd6ZqWC7QSAMEQe7nds2sSJfp8DuIRAutQBYm+00GkkOW+HJVylvpyNPKTNBO24ANrJJYsKukhTG3mmdjwW1YzzdPoxqazPQ0RE42CpJOGz1kTKckgT27NUSOFhWmVOJGPmU/4GwCjbHN4S5SULBrp/ohw/SLc8stIUV+ToFNsc36EiFbBXStPtDWj2zg0uP2n1GMpySBKoo3M6BBeEcwqTOx5IDS8YFxRBK0rRQ1dbaDXvAqtTY+bC3lE9ZmamnQ7UFe81DYafxg906H9XMEK7cw65SF0alA0+pa/eHxue+Hbf7DEdSQ4rf7oBrW1iRr1Ngs/YgbEcTzERghu3VUeMDahbVOXJglmrqDpvhlSSbDqGiIbUwsdfw2p3e6xjeIdS7A7oDsw6soqEmCew5MB1nQyoRo5hJ2CMzus5di2QxDLYsiQo6VFBQacdVzdcLBVsOrDcYUe8MtES3YP4Q0NGNB1OHYHqeT7Wlx96tgh35W4cKmkvFySTtzH2rhuxogmmDwIFhe3URcfX3D5tm06QTB3aO0o6FgPc6zsJWXZLXSRr+HAOoGg7M+sMRx+3waTx1tpheD/qCXjt+wja0kC8hxM8IId4TQnwghPj6nJ//LSHEO0KI7wshviOEuK7jc01jM+e185o+BFTXlDb1wHCUoFNJsnFvV7XRI5uMkw1R1wF2HVjYaNGb52PnQuVqI9wMNbDnwHSkoGf/vumIXBtZzNmqrwyvgoK920V07LWNnHe/o+mzYeInNAUOpv1aVUPnq/r7tua+2URo8iWEiAO/Dvws8Abwi0KIN0687HvAm1LKzwL/HPj7YT/XBhLxGBu5pPFDYNruHFY9sDOQTlc0rv6+aXt1pBbAe77npYYKxmldC2m8Zm8Yei0oB2ZctdXkEKwpXw3vGq/NgNd4KZQKKTr9kfF6UB0F4aDG5pyPtKO6B9ieahtSwbeU4p+mHTUFZs9Z6lGH8vUl4AMp5W0pZQ/4LeArsy+QUv4rKWVr/OUfAFc0fK4V2FA7dG0qW2lS9f5hHYKtcQg6xniAd2jVOgN6A7PjEKqaHJiNWgldyszEgVkg4qAnBQ126mbC3OuoYKseVIeSBNNUk0l0+kNavaEmsmi+AUO9f2gV1NLtIsrezXzwgbAwc7n2c9bxqIN8XQbuzXx9f/y9RfirwP817wdCiK8JId4SQrxVLpc1mBYeNtpcdTmwSZ2PYTJTbfYoZry7JMPA1hVDupSkyTwfg8M1e4MR9W74+j+w5BA0rV1Qc9/spB1Dd4xZrJvRpSSp9zMJHfV/4P1+Dls9pDRX56OrIBzsBOm6Mg7FdIJkXFhQmXsUNdT/2UqT2oYO8jUvJJu7Y4QQ/wnwJvBr834upfyGlPJNKeWbOzs7GkwLDxvTgHXVoag6H/O5fH1KEtgpstYTjZsf36CInS4yc9A8Xw7MhjITdowHTOe+2TgbdD1bMGvv9F7HcKoieOupP5TUOubSpLqUJFCjPEwHDnrKUyZ+wkKQHjbIAbtz32xCB/m6D1yd+foK8PDki4QQPw3818DPSSnPTfK2ZGEKu477uhRsdOTpIl+bk1SIhUNAUw0VmJW/dRFxgO18mt5gRKNrzoGp352uNKl5MtNlK58ONcYDvLlvmznzHXkVDcOXwc44BO+KnXDXeCnYIIsHk/q/8GTRVnmKEF59ZFjYsleLn8jZ8RO2oYN8fRe4KYR4SQiRAn4B+ObsC4QQnwf+Rzzita/hM61hK+/J3ybbXL26jmSo+7oUbMnfOg7YZDzGejZp1N52b0i7P9QUgZlP3ehO44FZsqirhsp7D/P3O+pyCGAvraszZW4yratz7doosq5qDHRK+TRH46GipqCr/g/sDN3V6Se8xreV8vUUpJQD4JeA3wXeBX5bSvm2EOJXhBA/N37ZrwEF4J8JIf5ECPHNBW8XOZTy5ttcddVJgJ1BoFrtNazUTbrbNDoEkwRBVzce2LmhodLskYgJ1rLh0njgrV3TDQ06BsIqbBoOdAbDEYetcPc6Kqg6n6rB7kxdw5fBzoBrHfc6KmzlU0hpth5Ue+BwTur/4Pm8Yij8iQlIKb8FfOvE93555s8/reNzXGA2AtO1kE5C56ZSEY2UMnRqZR5UXUfYzkwF02qHrs5MgLWM+ULVQ432bk2KrA06XA33OirMNjTsrWVCv988VJpdbmzltLzXVj7Frf2GlveaB3XPpQ6yKIQwPjvroKFPBbXRkaer/g+eTpOGvT1hEXR1bYN58qXfTzx/U+5XE+7PwLTI2uwhoOPAAs8hdAcjmobu7ap39dV1gNpUZp8taHZghqNxbXUdFlJNOh3CtoVxCNWGnoJwMO/AdKbxvPcxW1NX1bjXbNSoqYBaR+BgY5SHrsYh8OxtGLweS7ufsHS7iE2syNcZsFH4qVtOBnPFiTo7hGDcUm7y2U7s1eNwTRdZ66zrKOXsODBdaTzTaVI1EFZnKuSw1TNW56OzmQHMX9mjkyxmknFyqbhZ5auhT5mxodTp9RNm61e1+wnDa9cFVuTrDJhucx0MRxy1wt/XpWDaXvW+OuokwHxDg87RDWB+FpXOAzabipNNxo0rddpSC4YbGnSOxQBvTUkJR4bqfJS9utJYppW6SqNHPhUnkww310nBuL3N3qSDOSxMNwgMR5LDlj7lq2RYqVMBlG4/YbKhwTZW5OsMqNobUw5MZ10HzEQ0puxV5EtDWgzMNzSouo61jJbyRkr59OR3ZgI603hgx4HpcgiTy7UNrd1Jd5suMmOYLOpPO5pNmVeaXW3OFuwodbqe7aZhldkbOKs3iASDQbrGTlIwH+i4wIp8nYFUIkYxkzAW0eg+YCf3dhlapCYcgve+5tKkmzk9dR2gum4MDllt9rQRWxgrdYbWQm8wot7RM40fYC2TJB4TxtbCgcZuPDBfl6TrXkeFUj5F3WCdT1Vj7SqYv1xbJ/kyPTZn2pmpTwX13vd8+DXTgY4LrMjXEtgumCsKr2h2CKZr1HQWsIMN+Vu/kuQNkzQzDkHXVGgFk8qX7pRuLCaMTrlXqo/+VJO5taur/g/MXwauaxq/QimfNqbUdfpDGt2BVntNKnVqT2xrsnfb8CgPXZdqK2wZ3msusCJfS8CkA9M5pBK8+x3TiZhBe7tkkjFyKV1pPLObSveIkM2JA9Nv70hzXQeYvbLnQNN1J7Mw6sAMKV8mzwada3eq1JlTO7TaOzM2Rzemyoxmpc5U4KC51nYtmyARE0bXbjYZJ5vSV/+n3vd5wYp8LQEb5EvXoeXd22XO4eociwEzs6gMpknNODD99h61+4w01nWAV5tnPHDQONfIayk3Qw4qzR6pRIyChrlOMCXixpSvhn7VFszYK6XUXvNVGo/NaRkYm6P73FXvZTKIVJ+hA0IIo0OCz9O56wor8rUEbMjJm7nw9zoqlAx25OneVJt5799tMmLUrSSp99UN3QcseGuh3R/SPjcOzFyKvzpOi+mq/0vGVT2oOaVOV4oUpqUCJuxVc522dSpJOXP2TjtJ9St1JqDeV1f9H5hWmfXdJAHTuYcr5esFQynvzaIyJX9v5JIk4vp+FZuG1Q6dzjadiFNMJ4wcAv3hiFpnoDW1YDLVNO0Q0m+viVST7o4m9V6miLju+j8w68B077WSwTof3XOdZt/LxPM1EugYHJtTbfZYzyZJavQTppU6nc922vi2Il8vFEr5FIORpNYeaH/vioFri0wrdbrt9ZQ6/fZOxmJoToWAGfKlCtiVGqgDyuGaKLKuNnvEY4L1rD57twx25JkgX6Y68tS9jjoDh41skpgwc/+g7vl/s+9l4vmaCHRK+TTDkeTYwNgcnSNdFIySLwN+wvToEdtYka8loOTTA0OHgP5NZe4akcOWKQdm0CFolOo3cimEMBON6+4QArNT471uvCQxTd14YHbQarXZ1X7vXimfNqIkTeb/adxrsZgwdkNDxVDzhffeJtaCvgvhFUzWJRkjMwbqK736P1Nk8fm533FFvpaAyasYdKcWwCOLrd6QTl+vetDpD2lpvJ5FoWTIIZioSYrHBBvZpJFDQKVu9CpfZmvUTBBxMJcaM+HATJ0LoG+ki4KpjjwTzRcm126l0WNTY/0fGLbXyF5LU+sM6A30js1p9YZ0ByOtqi2YC3RcQQv5EkL8jBDiPSHEB0KIr8/5eVoI8b+Nf/7vhBA3dHyuLZiOwPQvUjOHgO7rWRRMRTS6Z5IpmFTqiukE6YSe9mwwTb70k5ltQ5O3dd/rqFAqpMbTx/XW+egei6FwnlTmQjpBKm5mbI4pZQbMpEmrmgvYYZrW1Z2GrhryE6YCHVcITb6EEHHg14GfBd4AflEI8caJl/1V4FBK+SrwD4H/Luzn2oQpB2ZirhOYs9dEUS2oy7X72h3YoQHlC7y0oDEirvmAXcskSMaFsTSpzhQpmLsY3oQKCp5D6A8l9a7eelBj9hZSRlLQ1WaPXErfXCfwxiGYulDZhGpr6soez0/ou/9XwZSoUDG0dk0FOq6gI+H9JeADKeVtACHEbwFfAd6Zec1XgP92/Od/DvwjIYSQ5+QpmopoTMx1AnO1B+rQ1h2BbeVT9IYjGt0BxYy+lFul2dN6PYtCKZ/i9kFD63uCmXo6Ibw6HxNDYSsN/dG4qZovU2RmcjY0eqxpXLsm7T0vKiiYtfczVza0vufsWtCJ43af4UiemwzJpJPUgJ9QgY7aa//ij+/zD37v/aX+/vWtHP/0r/8ZrTaFgQ7ydRm4N/P1feAnFr1GSjkQQhwDW8DB7IuEEF8DvgZw7do1DabpQSYZp2BgHELVEJkxRRZNTIWefb9qs6eVfFWbXTaySW3XsyiUCineumuGzFxcz2h/XxPqQX844ritPxpXSp3uy7VNpszV+9/Yzmt73+n8P/31lUdjZ65zX5joJAVzs7NMpB3TCTN+wsRMstn3062EmhhBA/MDnT/8qEql2eU//OylM//+3ppevxUWOsjXvB18UtFa5jVIKb8BfAPgzTffjJQqZiICM9HuPPt+uuVkk6kb8A6Z61v6HFi12ZtMIdeJUi7FYavPaCS1dvpVmz0+dWlN2/spmFi7qk5E9wGrUk26AwdTKWhz6oH+uU7g2Sul9/vT2flpopMUPHvvVJpa31P3hfCz2DIwNsecCmpWZdbZfAHTGyVmA53ecMRWPs1//5d+TOtn2YCOnX0fuDrz9RXg4aLXCCESwDpQ1fDZ1mDCgZnaVKbu7aqo9uyMvvZsMCfXmxjjAZ69uuf5SCmN1HyB6bWr3+GaqKkzMcYDDKrMBmpBAUqm0roGOknBTHem7gvhZ2Fmr5lpvlBz30ycDalEjLzG+j+YP+B6MJSkEudzaIMOq78L3BRCvCSESAG/AHzzxGu+CXx1/Oe/CPzf56XeS8HEfYmmuvFM3dtVNdCeDWbVA1PRLeitqWt0B+MozoC9Bub5mGq+ADOppmqzSzwmKGoOHCYq8zkhMyaKrE3NdQLYLqRpah6bYyotpt7TVNpRd+Bgau6bWgvm/MT0LOsPRyQ0l5XYQmjyJaUcAL8E/C7wLvDbUsq3hRC/IoT4ufHL/mdgSwjxAfC3gGfGUUQdJtUD3XUdYGZ2lrFoXG0qzS3PXgG7mVQI6CWLagK9GXu9eT79ob55PqYCB1AOTH+94mYupTVNDJBNxckm49rVGdOBg861a2quE5jZa6YyDuo9taugBub/KZhQFo2t3TmBTn840p6atwUtYaCU8lvAt05875dn/twB/pKOz3IFdQWOlFIbo/cKzBNGZFN1H6VOmNpUuVScdELvPB/Vnm2ULGo8ZKdznUwcsN57HrZ67Bb1FPSbdWAG0o6GUtBgps6n0uzxhet6u/HAzNo1NdcJniZflzayWt7TVNc2TG8X0eknTMz/UzBSy2zIT8wLdPpDSTL+gipfLwpmxyHowkGja8whmLgv0RT5EkJoT+tO27NNOgR9NV8ma6hMFNaaGuMB0xsa2j19qSZTaxf0p5rU/D8T9qrfl85uUlNznWBK6A40ps3N1it64xBqHX1+wlQtKJiZ+1Yx6ddOkMXzrHydT6sdwIQDO08OAQxvqoJeud5kWsyM8mVBPdDocKvNLpu5lPYxHjDb/arX4ZpyYCXNadJaxwscTBDbZDzGRi6p+RwzM9cJzMx9qzZ7xIRXcK4bptKkpvyEqXIaE8QWnq0HHQwliZXy9XxjGoHp3lRmFmkpn+K43ddW59Mfjqh1Bgbt1XsZuMl6OhPzfEym8Uw0CBgNHEw4XEP1iuDZq5PYmgwcQL/DNVnAboLMVAzV/8FsTZ0+Mm40Q5JPc9jqM9DkJ9T9v7bWbm+lfD3/MHUI6B6cp6A2q657u6ZzkvRHi6BfqTPVnq2g24EdNnukEzFymtuzwczaPTDUjQf6L9ceDEcctfpGiDhM166uBm6TaTHQ39BgcnSDieuxTHWSgpkZi6YzJACHLT0lFCYVfPAayZ4aNTEakVqRr+cbulNNUkoOjcrJetWDimGHoJvMqHqsc6MeGGrPhml6RbeyaOqA1X25tnIsJtdCdzCiqalGzaSSBOM0qWalLhWPUUjrHeMB0+ux9KbMDZ67mrtJpZTGurZBf2BmcgSNet+nar4Gq7Tjcw/dqZtae8DAUEE46K/zMZkWU+/b0jjPx7TypbtBwNQ0foCEkTofG8qXnkDH9NqdpEnPyV7bKmhO8Y+VJBOBA+ivqas0u8aIuO57db0RMdJ4hkTX8zXZSQoeuW33p804/dEq7fjcI5dKaJ3nY3qR6iaLNupQQK9SVzDUng3eVRe6Urpgrj1bQadSNxx345lSZgppb/yKvrVgnogDHGhyYCbTeODZe9jqMRrpS5OaXLvbhfS5qVfMJOPkUnF9SpLpoFezUmcjZQ7TPb3qdnxBoNOB2Ujjgb5NZepuPAXt8rdhh6C/zsdcUS3orfM5avWQ0txaUKNHdDW3TOdQGd5rugKzRo98Kk4maSZwKOVTjCQcaboeq9LsGQvKQH/gcNTuGzt3QaV1dam25mtXvc/Rt3Zn31c3TpbTDFZzvl4M6Lz2xHRdh+46HzXXyUR7NuiX602m8cA7XHoa63wOm+YdX55krwAAIABJREFUgvbo1sBFygpbGkePmE/j6Q4cusbGYsA0TaozrWtctdVEbA/HgYPRQEejUjf1E2b2mmpC0VVCUWn2SMb13/+rUDrhJ/rDEYmV8vX8w4gDOyd1PpWGN9fJ1ELX3dBgcqI56FU7uoMhje7Agnqgt6Np2+jz1e/ANnKmAgfPMepKO1YMjqABM4GOaZW53h3QHYQPdEyfu+DZqz/QMWNvMh5jPavPT1SbXaP1f1snzt3eYNXt+EJAL/kyKyer9z4/aTy9Ldomu/FgtqYuvMM1OZNMoaSxzse0QwCP2OlaC4etHuvZpLHaEN33O1abPUqGiCLoTTWpwKFkcO3qnPtmOuMAZspTTJck6PUTBhX8EyrzYCRf3Iu1XyTorJtRBeGm6jpAs72GlaS1bIJ4TGg5BKSU444mc4eAIkpaHYJR5SvNcCSpdcKrXyavk1HQee1JxTARB70lCaYd2CRw0JB2tEHEdc59s2GvznrQarNHzmD9H5yvvVZMPz33rT8ckTRwN7INhLJaCFESQnxbCHFr/P/NOa/5nBDi3woh3hZCfF8I8R+F+UyXKOXTdPojWr3w93aZVpJAdwRmrj0bpvN8dHQQ1rtee7bZaFFjNK7SeIYdwuxnhYFSeMwqdRr3msGhmgq6hgR7gYPZAvZJnc85UZJ01tTZyjjoqgc9b37CtL2TuW/NLlLK8cXaLyD5Ar4OfEdKeRP4zvjrk2gB/6mU8lPAzwD/gxBiI+TnOsGW5gjM/KbSN8/Hi2jMReOgb3aWFSVJo0NQCoTJ57upMdVUaXbZyJlL48GsOnM+9po3Oyu8etDsDekNRkbt1VnnY3q0gPfeOteunRQ/6KkHtaHa6vQTNgIdRRYH4xKK5AuadvwK8JvjP/8m8PMnXyClfF9KeWv854fAPrAT8nOdQOshYDiNB2qeTz90nY+6nuW8RGDVyQw1cw4hn4prm0VlKxUy+1lhYGvtgnevXViYVpJA39R40xPCFXQpdbYK2EGTats0W/8HuutBu1bWgg4/0R0MqXcHVlL81WaPwXBMvl7EtCOwJ6V8BDD+/+5pLxZCfAlIAR+G/Fwn0Kp2WNhUpXyK4UhyHHKeT7VlPi0G3vPV8WwPLKRC1CwqHQ7hoOFdz1I0cD2Lgs7A4aBhtp4O9BVZj0bqehY7ZCZsnY/aa1Zq1DQRWzBr71omSSImtNlrPnDQ1zzkKUlm95o2PzEZxG3aXk+p640vA39uC+6FEL8vhPjhnP++4ueDhBAXgf8V+M+klHOvUBdCfE0I8ZYQ4q1yuezn7a1AVwQmpfRSIYbJjK4p99M0noW04zkpYAd9Sl2l4dXTmWrPBv2pG9NEXFeKv9bpMxxJo2km8NaajjofGzVJ6v11qczxmGDd0Pw/gFhMsKnLXktpMQi/12zU/4F+P2Er0BmMyVfqeVW+pJQ/LaX89Jz/fgd4MiZVilztz3sPIcQa8H8C/42U8g9O+axvSCnflFK+ubMTvcykruGENgrCYboJwhax20gtqPc/bvfpD+dy86Vh04FpIYsWDthMMk4+FddUU9c1X/+nyyE0bRFxPWeD6aGaCrrqfKrNHpu5JDHD6oPONKn5+j89a7fZG9IdjKz5ibBrt2ptr6Wodwa0xoFOIvackq8z8E3gq+M/fxX4nZMvEEKkgP8d+MdSyn8W8vOcQledz7Suw7ycDOHVA1V3Y0vtOGqFk78PGj2KBu91VCjlU5Nrl8LA9FBNBU89CHfADoYjDlt94wdsLpUgk4yFdgjTa7HMq7YQ3uHaqP8Dby9Xm+HnvlUsKEmgUWW2EOiotRt2r9mq/9Ol1NkM0gH26x2AF/Z6oV8FviyEuAV8efw1Qog3hRC/MX7NXwZ+EvgrQog/Gf/3uZCf6wS66nzsReO6N5X5aHz284LCxgELetOOJqfFK+hYu5OaJMMpaPDUHx1rwXsvS2pHyECn2vTq//Ip84GDjvsdbShJML6yJyQRt1X/B97aDe8nVOOQpRq187LXxu//+Nh7Pud11ESoCl8pZQX4qTnffwv4a+M//xPgn4T5nChBh8OtWlqkuq7sqTR6xAze66iwmffe3zt0ioHfp2p4wKrCVj5FY3ztSRiVrdKwRxbL2tJiNhxuioNzFo2H3mtjMmOy/g+etjfMs6k2e3zy4pousxZCR+Cg6v9sqMw6/YRpe9W5G95er/5vLWPaT3jr9UlNKV/nk3ydT6sdQkedj62apHQiTiGd0BLRlPJpC3UdmpQva6mQ8Pa2egPa/aEVsljKp0PPHrJKvjSkSW2RL13qgS0labugpyOvYsleVefTGwSvB7WlzMB0HEIY2LI3nYhTTCe0kMVSPmWl/g9mydeLmXZ84aDDIRxYKqoFPRGYV2Bt54CF8OTroGG+Gw+gpJS6EA7MVocQTK/ACTMOoWJhhppCKZ8OTw4a5q9nAe9+x5yGhgabKXP1eUExGI44bpuf/wd6modsEXH1GTpS0Oq9TKOk4XqsAwvz/2D6PFbK1wsGHepBtdkjm4yTNVzXAfrkbxsOYTMXnsyoug47xDa88mXjaiGFzVyK7mA06RIKAvW7sWHvtgayaGNIpYKevWbHXh0NAofjxhgbZ4OO0SNWA518+PsSq80e6USMnDU/Ed5eG892I5dCCHi8Il8vFrYKKZq9IZ1+cAdma5GCnit7bKUWEvEYG7lw154ct1Vdx/lQ6mxcLaSgY8p9pdklYaGuA6Z35DW6we93tDFUU2Ernwo9kf+waUdJmlw3FeJssKnMTMb8hCAItkYhgJ67SdVNEqbr/0CPn7Dl1+Ix737H/Zq3FhKrtOOLAS0O15KSBONxCCHnfFUa3UmNiGmU8qlJR10Q2OoQAk1kxtJA2NnPCEMQVD2d6boO0DPl3mqgUwjXndkdDGlYuJ4Fpvc7hiEzFUu1q7OfEW4t2LNXh1JXbXaNjxxROE/lKeDZu0o7vmDQdQhYS4WETN30BiNqnYFVpS5MND5Ni5kni+vZJPGYCOnA7NX/qWdyEOL5HlhqZoBZshjc3nK9y07RYuCggYjb6MaD8B2EVYtrV0vasdmjYGH+H+jyE3bm/4G35g5bwf1Ef6j8hL29pm6TWBXcvyDQUStRbdipSQLP3jDXnhy27CkzoLpJw5MZGwQhFvPmvh3Uw6Udcyk79X+KhIRSvpr2VNCpww1m72jkXc9ii3yp1E1QB6Z+L1bJooa0oxpVYBIq0DkvKqiOe4Btp8z7Q0mtEyxNOhlmbMlPzD6XlfL1gmCaCgnmEGzd16UQ9tqTA4s1SeA5njBKx6SGytLz3SmmQ83OsrkW1OeU6+HSjvbsDZd2PGz1GI6kPbJYSNEbBq9RU78Xa2Qx5DiEcr1LTNg5G2LjOp+wSp0t8rWtYfRI1Sb5CkkWJ41DFtOOCivl6wVB2Ct7WuP7uqwdAiHrfGzWJAHsFDJUm73A9ztOlC/DFykrbBfSocjMgYV7EhXSiTjr2WTImi979oZVmRWJt6ckhZudpdaRjU5SGI/yCKEyl+veMOO4hfo/UMpiOHutrYUJmQlmb6c/pNUbWq35guBBus3mC3h61M1K+XpBsJZJkErEAqsdNtudAXaLGSC42mFrGr/CdjEcua00emzkkiQsbUhPqQvXgWXr2cJYqQu4Ftq9Ic3e0BoRD3sZ+ERJsqh8QRiyqMiXPXJ72OoHvt+xXO9ae7YQvqauXO+ya4l8qXuAwxNxO/ZO60FDZkisBemrtOMLByEEOyHUDkXabB1aKtILaq/1tGMhnL0uyMxBoxvYgdlM44GnqgRWQZt2lRlQDSPh1u62xZovCJ66Kde7rGUSxgfCKmwVUgxHkuOA9zuWG11rzxa8tRD02faHI6ote/V/Ez8RcK/tj88/W2Rxdy2sn7DX6HTyc1ajJl4ghFEPbNd1lPIpYiLcpkrFY6xlQ10DujQmZLHRCfT3Dxp27nVU2Cmk6Q+DOTCv/s+yvcVM4LUwvVrInr1hLtd2sdcgeOqm3LCXFoPwU+5tK19hyEy12UNKe2sBzpef2MqnQ/mJcr1Lajy+xAZmSX9qpXy9OAi3qTxSYSuiiccEW6EisA47xbSVQX8w05EXsIOw3OhaVWa2J2TR//OtdQb0h9KqUucpX8GebdVyRxOowaXB03ipRIxi2k7gEPZ+x3LdXicpTNWDIGeZlJIDy2Rxp5im3hkEGnBtOwUNevyErecbjwlK+fREcfML237iaeXrfNKYUFYLIUpCiG8LIW6N/795ymvXhBAPhBD/KMxnRgFhNtW+6hCyHTGGiGhsHrAThxBUPah1J3VuNqAO84MAz9d2jQ94a7fRHdAOMHpkYq9N5asQ/NoTpczYcgjZlFejFrxuxl5aDKYB4H7dv8p83O7TH0o39tb8P1/bShJ49gYlMzY7SRV2Qyp1tom4wova7fh14DtSypvAd8ZfL8LfBf7fkJ8XCewW01RbwTryyvUupby9DiEISRZrdjdVJhlnLZMIZG+7N6TeHTg5BIKQReVEbKmgEK6wtmy5qBbGd6kGHBJsuyYJYHctE8rh2iUHwZtxXJCZnRBk0ZW9QTu3yw27naQQbmyO7bWbn5mLmIy9gMoX8BXgN8d//k3g5+e9SAjxRWAP+L2QnxcJ7BTTSBmsI2/fYseNQij5u3F+7N23nNKFcA0NE3vXXDiwYGSxkE6Qt5TGAy9NGnT4o+2aJBiv3QDKTLvnXS1k04GtZb3O7SBrwUUaLxRZdKAyK3uDBDr7NTdrN4iqCPb92qyabeOqMxMIS772pJSPAMb/3z35AiFEDPgHwN85682EEF8TQrwlhHirXC6HNM0cwnTkletdq84WphGNX/WgNxhRbfaspvEgDPkaK0lr9uxdyyRIxYONHpkoXxbt3QmjfDlYu2GK2L00nj2VDmBvLcOTAMqMixS0EMJLjdUCKEmWp/HDNEgJFjh0rHaSQrjAzHbzBXhBa5DO7f7QjZ847ziTfAkhfl8I8cM5/31lyc/4G8C3pJT3znqhlPIbUso3pZRv7uzsLPn29qGcZZCOvP16x35EM+7IO2r568hTDsG2w90O2CDgIo0nhAil1GWS9grCIZxDeFLrWFdBg065H44k1aZ99WB3rB74DXT2HaTFIHhdkos0XimXIh4TwdKOjsgMBK9Rc5FxGIwkRz47t21fi/W84MxTX0r504t+JoR4IoS4KKV8JIS4COzPedmfBf68EOJvAAUgJYRoSClPqw+LNHYCbqrRSHLQ6DlRvsA7gDZ9dNbtO0gtwPlKO4LX8RhUqdstZqwVhMNUSQqUCql3+fy1Dd0mnYqtib3+yFe12WMk7c34Utgtpmn3vRRiMbN8272LNB54St2t/Ybvv1eue52kaxl7gUMsJtgupAKTGdvkIGg96Ggkndq7X+/4GgKu1q71c7cQbsC1a4RNO34T+Or4z18FfufkC6SU/7GU8pqU8gbwt4F/fJ6JF0yHTPp1uNXxXXMuyAz4t3eyqRyQxUZ3QKvnr85nv94lMb4DziZ2Ao5veFLrsGf52SbjMUr5lO+1IKV0pHypWVTB1q4LMgP+U2Ou1IPAaUfLnaQKu8VMIFXcIzN202IqheyXLB61+wxGdjtJIXhNnfr32bb323/zJ/n23/xJq5+pE2HJ168CXxZC3AK+PP4aIcSbQojfCGtcVKHuyPN7CJQd1CRBcPI1VZIs2zsZ3+CP0KjOTNsFmGFq1FzUSQSZcl/rDOgORhNyYQsqAq/6JLe2p9srKHL6xCehKde7CGHv2jGF3bUMtQCzs1yk8WCa1vULF80XqUSMzVzSd3mKi5Tu7Of5DtIdlads5lPc3Cta/UydCEW+pJQVKeVPSSlvjv9fHX//LSnlX5vz+v9FSvlLYT4zKghyCLis64BgEY0QdkcLQHC5fr9uX5kBjyxWm12GPgtVy5bHeCgEIYtKHbFtbzoRp5hO+B5c6kr5CnpNS7nRpZRLWb+nLowq7oR8rfmvUWt2BzR7Q+vkALzA1b+fcBT0BuyEVv8+mzPJngeczwEZEUCQmSiucuOFdIJM0n9H3n79PDoE+0rSTjHNSPpLjbV6A+rdgROH4NVK+FQVx78L28oXeOTfL/lypXyp9efX4TojMwFnZ9mebq+wU0hTaXYZ+JidNUnpWibiEM5P2H6+hXSCXCoeIHDwasRSiRWd8IPV0wqIQOqB5SsjFIJ25JXHV0bYRnDly/4oBJgZXOojTaqc854LshjgxgOVRnNBvkr5lO9RE+V6l2wy/tQwRhvwxhnEApEZm2MmFHYDkMXBcESl2XNi785axpux6IOMuyIzECxD4tLeYKq4/ZTu84AV+QoIr0W746ulXA2pzKXsdQgpBHG43lwnB0pHgEtepzPJzgdZnM4kc0AWxx15ze7yDQ37jlRb8MZN+B1ofNDosl1MWS8I92Zn+Z9y7zKNB/5STS4uqVYIUkIRBTLjy0/Uu+RScQoWR9Ao7BTSvgMHV0HveceKfAXETjFNpz+i4cOBuZgWr7BTDLipHNjrXfLqryNvMpPMUdoR/DkEV3UdME2/+HG4T2od69PtFYKs3bIjJQk8guCn4F5KN6MFwJudlfA5O8vVCBoIliZ1VWurPrM3HFFr+/ATjtYCeGT8vNT/nXesyFdABHG45Zr9u+YU/MrJrmbNKGz7VOpcKjOTy8B9kRlVQ2XfXpU69EMQXBFxgAtrGQ5bfV8deY+PO1xwoNqC93z9ENtG1+sk3bbc2AJqdpa/1JiL6fYKQWYslutd4g5G0ECw+yhddGYq+M2QuAwczjtW5Csgdgr+5/k4Vb4KngPrDZYrVD1s9RiMpFOlruwnuq3ZvydRIZ9OUEwnfJKZDqlEjPXs8oM4deHCuv9xCPu1jrPUgiJRfhzuk1rXSX0a+L/f0WU9HfjvIHTVSQrBOvLK9S5b+ZTVS6oVgszO2ndUawve8/UzeqTWHtAbjlZXCwXAinwFRJCW8v2a200Fy082LztM44HncJ/4cGBT5cuR2rGe4fGxj+i25mZIJUydvB97Xc0kA+/ZAjxekizWO30a3QEX1t2RmbqPIcGPxr8HV0qd3yuGnhy7C3TSiTgbuaS/jIPDFHRQsugq6PVLFl01kT0PWJGvgPBbNzOZNeOKzIzVjmUd2PTSZzeb6uJ6hv16Z+mW8v3xkEoXqRvw7H3kM43nIuUIUMwkKaQTE6d/FtR0e1f2XvRJvpSSdNER+drz2UGofg8X17PGbDoNO8WML5X5Ua3DVj5l9ZLqWez6rAF8dNxxthb8Bumd/pBaZ+A8SF/Wr7kan/Q8YEW+AmIjlySdiPH4uL3U61123MD0YF9W7XBZVAtwYT3LSC7fQViuew4hYXkmmcKFtcxEEVgG3lU97qT6vbXli8Lr3QGdvrvUwqRGbcnn+/jY3Uwy8N9B6FJJAs9xVpq9pQOdx8cdZ6oiqAaM5ZWkx8dtLm64sbc4nrG47F5T5/MFR0Rc/V59+4kV+fKNFfkKCCEEF9czPFxykT4ck7RLjg4tFfk9PFqOLD5xWEMFU3uXVWe8q4XcOYQLAZQ6l+3ZF9YzPlRQt2thLZMgm4wvba96nbs0nqoHXc7eRzVvSKUzJWktjZTLX17uUkkCT1lcVlVs94YctvrOVEXPT2SXVsWVn3D1fKfn7nJ+YurX3Dzf84wV+QqBi+tZHi1JZh4djVMLG24W6Xo26TmwJcnMo+M2G7mkk5lk4D8Ce1J3lxYDz95llbpOf8hxu+9Uqt9bW75GbTIQ1hGZEUL4IotKjXZW8+WzI89lZyZM06R+nq9L5evihrcWlrnOyzURh3FJgl8/4ej5Kj/x8GhJP3HUYSOXJGt5mPHzgBX5CoGLG8s7MKU4udpUSqlbVkl6dNRxFi2Cf+Xr4VGHS46ILUwP92XWw7Sezq1D2K8vdx/lk8lMMpdkMb182rHmOQRXStJGLkkq4S/V5JLMqH2zDEHo9N0qSeAFvcPxKJyzoP5NrtKO4Nm7LJl5PKlXdKjUbWR4XFtS+TpqO10L5xkr8hUCl9azPFnSgT08dlukCp4SsKyc/OCozWWHB9Z6NkkmGVvKIbR7Q6rNHpddki8fSt2D8b/pimOyOBzJpa7tUQTYlfIFY5XZR82XS6VDCMHljezk93wWHtfcki+1b5ax13VnJgSz1yVBuLyxfEnCw6M2m46VpEs+yOLD446zUprzjlDkSwhREkJ8Wwhxa/z/zQWvuyaE+D0hxLtCiHeEEDfCfG5UcHHDc2DL1HY8clj0qXBxPetLqXOpJPmplZjUHTiObmE5pU45DZfPV9m7jAN7cOg5BBfT7RUub2R5XFvOgT1ynBYDby0u82w7fS9wuOiQzKxlE+RTy6WaHjmuSYLpvlmmfvWx485X8EpNRhKeLKPUHbvNOIC/ID0Kfu28Iqzy9XXgO1LKm8B3xl/Pwz8Gfk1K+UngS8B+yM+NBFSR4VKHluM0HngH0DJKXaM7oNYZRMLeZZQvdQi7LPrczHlK3TIO4cGh+1TI5U0f5OuoPXm9K1ze9FJNy9Ql3T9sc8W1vRvZye/5NEyUGceBzqWN7HJkRqmgjmu+YLmicKUkucw4TEooljzLXAaR4DWF7de79M8IdFq9AUeOU9DnGWHJ11eA3xz/+TeBnz/5AiHEG0BCSvltACllQ0rZCvm5kYDfQ8C1PLusUvfoyL2S5H3+cqmbhxFQkoQQXNnMcX8Jh/vwqM1OMU064c4hKDK1jL0PDtvOu5kmqaYz7K13+hy3+1zZzNkwayEubWTZr3fpDk6fFH7/0DsKrzomi5c2shMF+TSo9eIyxb+WSVJMJ5ZU6jrOxjYoXPKZJnVNZi5uZJHy7Bsw1PN3uRbOM8KSrz0p5SOA8f9357zmNeBICPEvhBDfE0L8mhBirtcRQnxNCPGWEOKtcrkc0jTzuLi+nPxd7/SpdwdOyQEwcUhnOVx1SLjeVFc3czypne3AHhx1iAl33W0KVzaz3D86O67w6uncPtu1TJL1bPJMMiOljIzyBWc7sEk9nWt7N5abq6f24pWSe7K4jPJ1/7DFTjHtVEmC5QOz+4ct58R22eahZnfAcbvvPI03HUt0RpAegRT0ecaZ5EsI8ftCiB/O+e8rS35GAvjzwN8Gfhx4Gfgr814opfyGlPJNKeWbOzs7S769O6xnPQd2r7qcQ3BNvtQh9HHldIIQhVQITB3oWQTh4VGbvbUMSUcDVhWubGaXU5IiQL7AIwhKeVmEo1afVm/o3N5lla/71WgEDkvbe9giERPsOR5SeXkjw0Gjd+adfveqbedkBjwV/yyyKKX07HVMbIuZJGuZxJlr4d54L15zbK/6/HvV088G9e9x7dfOK870VlLKn5ZSfnrOf78DPBFCXAQY/39eLdd94HtSyttSygHwL4Ev6PxHuMTVUpaPz1ikiuy43lSXN7MIMd3ki3CvGg2HoA7NM5W6w3Ykoq8rmzmOWn3qnf7C10RFSQKPLJ4XJSmTjLNdSPmw1/1eg7OVuvuHXsGyq5sZFJYtYr9/1HL+bGG5QOeg0aPdH0aCLF7byi3tJ65GYO0u4yc+HvuJKJy95xFhd/w3ga+O//xV4HfmvOa7wKYQQklZ/wHwTsjPjQyulXJnRghq013fcrup0ok4e8XMmYfA3WqLK5tZ5w7hask7NJc5BFwTW5hR6k5xYAeNHr3ByHn9H3iH7P3DNlIubsCY1vi4f77LjG+4f9ginYg5u+NT4cJ6BiHODhzuH7a5EoFnqwKd086GwXDEw6POZF+6xPVSnuN2n6PW4qn86txwrXyBZ++Z5KsajSA9nYhzYe38+InzirBP7VeBLwshbgFfHn+NEOJNIcRvAEgph3gpx+8IIX4ACOB/Cvm5kcHVkldkfVoH4cfVFsVMgvVs0qJl83G1lJ2kZhbhbqXJta28JYsWY7eYIRkXp6Z1u4MhD4/bXI+AvZOaulPsvVtpAkTG3lZvyFFrsVKn0pKulS/PhrMbGpSqKISwZNV8pBNxLi7hwO4ftiLxbFVgePeUkoRHx95UedfKDHhKEpxurwqKo0C+PD/ROtVP3Ku2KKYTbOSi4CeWEBUqrUg82/OKUORLSlmRUv6UlPLm+P/V8fffklL+tZnXfVtK+Vkp5WeklH9FSrncJWLnANdKOXrD0amdIXcrnjLj2iHAeFOdoiRJKblbaXHDsUoHEI+JM+uS7lXbSAk3tt3bq5zoac/3owOPfN3Ydk++VIR995RD9qODJuvZJJt5t0oSeL/je9XWqS3wdyutSJAD8H7H6vc9D53+kCe1biTSeDuFNLlUnDuVxfYq4hsFh3tjHLyctnYn9kbg+V7fytEfylM74z+uemQmCn7iWmmJNGm15Tybc56x0gtD4toScv29CC3Sq5s5Htc6CzsIvZqlgXPpW+GsCCxKStJWPkUhneDOKQ73TqVJPCYioXa8NCaAHx00Fr7mo4Pm5HWu8dJ2gcFILlS/pJR8dNDk5Z1o2HtjO38qmVFnRhQCByEE17fySylJUVi7k3P3tOdbabFdSEfi3sHrS/iJqJRPgPd8n9S6CxswjlveSJfrpWjstfOIFfkKiekhMH9TDUeSe4fRkWevb+WQcnEny91JfVo0NtVL23lul5sL65LujJ/7jQjYK4Tg5Z08t08lX17ru+vOTPDWbjwm+Kh8ir0HTV6ODPny9tAicrtf79LqDaNj71aeo9biuqTbZY/0vrxdsGnWQtzYyp1KFj88aJCKx5x3kgJkU3F2i+lTyeKdSpNrEahPg5maugX2jkaSe4ftSTrVNc7qeLxb9dZJVPzaeYR7D3DOcXkjSzIuFjrcR8dt+kMZmQjhlR3voP9gf77aMVWSorGpXt0tUO8OFl6ie7fSpJhJsBmBOgnwnu+HC54teMQhKsQ2lYhxdTPLhwvWbrs35OFxJxIpUvCUL2DhXvtQkZmdaJAZtYfuLHC4H45Jb1SUuutbee5VF9clfbjvqaBRKbC+vpU7Ne34YbnBq7vkBBncAAASCUlEQVTRWAuXxn5i0Vp4cNSmNxhFIoiEqSq+aK8p0hsVP3EeEY1ddI6RiMd4ebvAB/v1uT+/NXbEUTkEXtk9nXx9dNBECPcdNwoTslieb++dSosbW/lI1EkAvLyd5+Fxh1Zv8MzPpJTciVAaD7xDdpHypaLbqNi7mfPmJS1SvlR9VVTsVXYssvfDcoMLaxmnd2bO4sa4LmnRuInb5Qav7Ebj2YKndt9esHaPWj0OGj1u7hYtWzUf8Zjgpe38wnNXff+1vfPhJ27tN4iJ6Oy184gV+dKAV/cKE5J1Eu8/9khZVDZVIZ3g0npm4aZ673GdG1t55xOsFRT5WqQmffCkHhnlAKaqy7xC63K9S7M3jEQzg8JL2wU+Opif1lWkLCoHrBCCl3YKC4vYPyo3ySRjXHB4SfUsrpZyxMRi9eB2OTr1aXC6w+0NRtyttib7MQp4/UKRg0aXavPZtO4HEQt6AW7uFXn/yaIg3ft+VOwtpBNc3sgutPf9x3WuR8hPnEesyJcG3Nwt8HG1Nbc48f0nDXaLaTZy7rvFFF7ZLSxUkt57XI8MUQTYW0tTSCcmKZpZHLf6PDzu8MmLaw4smw/lTOdF5O+OifjrF6Jlb7s/nHv1ya39BiJi0e0rO/mFDuH2QZMbW3lisWiooJlknBvbeX70qPbMz6SU3C43IkW+Xr/gqUTvPn7W3ruVJsORjBz5AvjRHHujSL5e2y1y77A1VxW/9aTBTsT8xKu7BW49WSAq7EfLT5xHrMiXBtzcLSLltOZkFu8/qfPaXjSkb4VXdwt8uN9kdKK2o9MfcqfSjBQ5EELwys58uV4dup+4EJ3n+9J2nphgLkF456Fn7xsRIovq2b07hyC8/fCYl7bykUmLgffs9utdDhrP1gC+87AWKSIOnr3vzHm2T2pdap0Br0aIzKxlklzeyPKjR8+uXbX/IkW+xueqyi7M4tZ+g0wyGs0BCq9fKCDlfGXx1n6DmxEiiuBlaz4sN56pAewOhtyttCLn184bVuRLA26OI4CTUcJoJLm1Hz3y9dpekXZ/+Mw8qg/2G4zk9FCLCj5xYY23Hx4/kxr70fjQjZLDzSTjvLZX5AcPjp/52buPalxaz7AekeYAgDcurSEEc+19+2GNNy5F59kCfOrSOuDZNotyvcvjWodPX153YdZCfPLiGvcP29ROXDmlnvdnrkTN3uJcJenthzXiMREpJWmnmGYzl+S9OYHO+0/qvLJTiIwKCl7aEbxsyCyklHwQQfJ1c7dIdzB6puPxdtlTQaPm184bVuRLA17azpNJxvj+/acd2J1Kk05/xOsXorWpPjs+8P/k3tFT3//RJC0WrU31Y1c3OGz1n5l0/6PHdTZySXYd30F5Ep+5vM4P7j9LFt99FD0yk0sleGWnwA8fPO1wj9t97h+2I2evUg3fOUG+fvjQ23ufjqi9J9WkH9w/IibgjYvRIl+vXyjyYbn5zBzAP71/xOt7xUjMzFIQQvDaXnFybimMRpI/uXfEj13dcGTZfFwv5UgnYs+s3dsHTRrdQfT22tie758IzJRKHjU/cd6wIl8akIzH+OyVDf7o48Onvv/WXe/rL1zbdGHWQry+VySbjPO9j58mX9/7+JBCOhGpgnCYksU/vf+0vT98cMwnL6xFptNR4bNX1qk0ezycqaPq9IfcPmhGSqVT+PQlT1mchXIQSmmKCtZzSa5sZp+x9+2xg4iqA3vnhL3ff3DMaxEjM+ApdcORfIosSin50wiSGfD22tsPa0/V294+aFDvDPh8xOxNxGP82Bw/8UdjP/HF69HyE5+44PmJP777rF8rZhKRSkGfR6zIlyZ88fombz84fuoQ+KM7h2zkkpFbpIl4jM9cWX9G+frDj6p88fpmZOb4KLx+oUg6EeNPZ+ytdfq8/fCYH3+p5NCy+VCprx/MkMU/vnvIcCT5XMQcAnj2PjrusF+fkkW1Nj4VMTIDnrL4vY+PnlIWv3//mBtbOYqZ6KR0AXaLaS6uZ/junakDk1Lyg/vHkUuRAnzphref/uB2ZfK9O5UWtc6Az12NoL0vbdEbjJ7KOqig8vPXorfX3rzh+Yl2b+onvvfxIevZZGSG7Sok4jF+7Oo6f3xSVLjj+Yl4hFK65xHR8rLnGF+8tslgJJ86BL57t8qb1zcjVXeg8PlrG7z9cEoWK40ut/YbfCmCZCYZj/Hpy+sTJRHgD29XGUn4sy9vObRsPj55cY10IsYf3K5OvvevPzggHhP8RATtVb/zf33rYPK9/+/9Mp+4UGS7EK2ULsC/9+o2D47ak5ET/eGIf/thhZ94KXrPVgjBn3t1m3/z4cGkweWD/QaVZi+S5GB3LcPLO3n+7Qz5UsrMZ69Ez94fv+GpRX/40dTe7907ophJRI7MAPz4jRKDcVpU4Y/uHvKFaxuR9BNfvL75/7d350FdnGcAx78PCCJqBAHFoBwK8YzxwCOi1ajxSM1hmtZ0zNSYw0zbadMj09pkJm06k5m200naJLbTTmo1neYaE41mphOpEjXGKBCPiBhBBUXkUEDjRQSe/vFbKCWINsTfvsDzmWF+u+9vcR/30d1n3313lwOlZ5uKxZoLn3Oo/BzpjvXSdURWfH1FxiVFEyKwraASgIqzlzhSeZ7xSe4VMxAoWi7Xa9MBN7soUChMHuxmvNNvimPP8ZqmF5jvOHKa8G4hTh7AIsJCmZYWS+aB8qbeme2Fpxg7KIpeDt052GjUjX2I7dWdrE8D/3bP19aRU1zF9JvifI6sddPTAnFtPRSIN7e4ms9q67htWD8/w7qiqamx1Fy43HTXY2Z+OQCzhvX3M6wrunVwDNlHq5peYL4xr4z4GyKcuxEHICoynGHxvZtOdBoalM35FUxKiXGymBmXFI0ITcXtyTMXKag4R3qym/vddK9Y3HEkcJxo3M6uHtc6knYVXyLSV0QyRaTA+2y1HBaR34lInojki8gL4togna9A357hZKTGsnb3CRoalLc+PgHA3JFu7mAzUmOJigxjw75SANbuPkF0ZBg3J7hXzADMHxUPwHt5ZdTVN/BeXhmTUvo6+5C/20f050TNRfJPfkbZmUvsO3GGjNRYv8NqVUiIMGNoHFs+raCuvoHthae4XK98zdHiKzEmkuSYSDYdrAAg62AFYaHC1DQ3t++U1ECPXOaB8qbP0QP7EN/HjYfBtjQtLZbzn9ezraCS87V1bDlUybxR8U4WMwDTh8ax48hpys5cIqe4mrKzl7jzlgF+h9WqPj3CuHVwDGt3l9DQoLyzpxRVWDDazXgzhsQSHRnG2t2B48TbH5cQ2yvcufFpHVF7e76WA5tUNQ3Y5M3/DxGZAmQAo4FRwARgejvX66R7xyVQUn2RLYcqeSP7GBNT+jrznrmWwkJDmD9qAJkHytl7vIbMA+UsmpBIeDc3O0PT+vdmSFxPXtt1nHf3naSk+iIPTE7yO6wrmjmsP6EhwsrtR/nL1sOEiHDf+IF+h3VFd9wcz9lLdby26xgr3j/MgD4RpCe7u4O9a0wC2wpOseVQJa9nH2daWpyTvYoA/XpHMHNYP1bvKOKDglPsPlbDnBFunpQBzBren/gbInh521HW5JZQW9fAPO/kx0WLJybRoMqrO4t5dWcxEWEhzB7u7vZdNGEQx6susvlgBWtySxifFO3M+15bCu8Wwp233MjGvDL2nzjD5oMVfGPcQGePEx1Je7fg3cBqb3o1cE8ryygQAYQD3YEwoLyd63XS3JHxJET1YOmqbIpOX+DBKcl+h9SmpRnJANzzp+2EhgiLJyX6G9BVPDFnKPknz/KTN/eQEtvT6R1sXO/uPPa1wazJLWH1h0XcOzaBQY68L7M1tw3tx62DY/jVhgPsPV7Dj2ffRPdubvYqAjw6LYXoyDAeWpXNudo6ls8f5ndIbfrBzFRqLlxmyd93kRDVgyUO7xvCQkN4aGoyHx4+zTMb8piWFts0EN9FiTGRzBrWnxezClm3p5SlGSlOPRi4pbkj44m/IYJHXsmhsOIcD09N8TukNi2eFDjJXfDiB4SECPdPdPs40VFIa+90u+ZfFqlR1ahm89Wq+oXTZRH5PfAIIMBLqvrUFf68ZcAygMTExPHFxcVfOja/lFRf4Mm1+1k49kYWjnW3p6PRlkOVrPzgKD+cldYhupJXZBVSfPo835uRSrJDr71pTW1dPU+vyyO6ZzjfnT7EqYertqbo1HlWZBUypF8vHp022Pm7mXYdreKt3BLGJUWxaIL7B4T1e0vZmFfGg1OSnR3j06iuvoFVHxaRXVTFswtvdvLGi+bOXrrMcxsPUd+gPHPXSGcvkTY6UXORp9ftZ+7IeL41YZDf4VzVjsOneSmrgCfmDGWsY49OcomI5Kpq+jUte7XiS0T+DbTW5/wUsPpqxZeIpAJ/BBZ5TZnAz1V1a1vrTU9P15ycnKv/DYwxxhhjfPb/FF9X7ZtV1dltrKhcRAao6kkRGQBUtLLYQuAjVT3n/c6/gMlAm8WXMcYYY0xn1N4xX+uBJd70EuCdVpY5BkwXkW4iEkZgsH1+O9drjDHGGNMhtbf4+g1wu4gUALd784hIuoi87C2zBjgMfALsBfaq6oZ2rtcYY4wxpkNq1y0hqnoamNVKew6BAfaoaj3wWHvWY4wxxhjTWdjDOowxxhhjgsiKL2OMMcaYILLiyxhjjDEmiNr1kNXrSUQqgWA8ZTUWOBWE9Zirs1y4w3LhFsuHOywX7nAtF0mqek0vxXW2+AoWEcm51oeimevLcuEOy4VbLB/usFy4oyPnwi47GmOMMcYEkRVfxhhjjDFBZMUX/NXvAEwTy4U7LBdusXy4w3Lhjg6biy4/5ssYY4wxJpis58sYY4wxJois+DLGGGOMCaIuW3yJyDwR+VRECkVkud/xdAUislJEKkRkf7O2viKSKSIF3me01y4i8oKXn30iMs6/yDsfERkkIlkiki8ieSLyuNdu+QgyEYkQkV0istfLxTNee4qI7PRy8YaIhHvt3b35Qu/7ZD/j74xEJFREdovIu9685cInIlIkIp+IyB4RyfHaOvx+qksWXyISCqwA5gMjgG+LyAh/o+oSVgHzWrQtBzapahqwyZuHQG7SvJ9lwJ+DFGNXUQf8VFWHA5OB73v/BywfwVcLzFTVW4AxwDwRmQz8Fnjey0U18LC3/MNAtaqmAs97y5mv1uNAfrN5y4W/blPVMc2e6dXh91NdsvgCJgKFqnpEVT8HXgfu9jmmTk9VtwJVLZrvBlZ706uBe5q1v6IBHwFRIjIgOJF2fqp6UlU/9qY/I3CgScDyEXTeNj3nzYZ5PwrMBNZ47S1z0ZijNcAsEZEghdvpichA4OvAy968YLlwTYffT3XV4isBON5svsRrM8HXX1VPQqAgAPp57ZajIPEulYwFdmL58IV3mWsPUAFkAoeBGlWt8xZpvr2bcuF9fwaICW7EndofgJ8BDd58DJYLPymwUURyRWSZ19bh91Pd/A7AJ62dmdgzN9xiOQoCEekFvAX8SFXPtnHSbvm4jlS1HhgjIlHAWmB4a4t5n5aL60REFgAVqporIjMam1tZ1HIRPBmqWioi/YBMETnYxrIdJh9dteerBBjUbH4gUOpTLF1deWO3sPdZ4bVbjq4zEQkjUHj9U1Xf9potHz5S1RrgfQLj8KJEpPEEufn2bsqF930fvng533w5GcBdIlJEYDjKTAI9YZYLn6hqqfdZQeDEZCKdYD/VVYuvbCDNu4MlHLgfWO9zTF3VemCJN70EeKdZ+3e8u1cmA2cau5lN+3njUv4G5Kvqc82+snwEmYjEeT1eiEgPYDaBMXhZwH3eYi1z0Zij+4DNak/L/kqo6i9UdaCqJhM4LmxW1cVYLnwhIj1FpHfjNDAH2E8n2E912Sfci8gdBM5oQoGVqvqszyF1eiLyGjADiAXKgV8C64A3gUTgGPBNVa3yioOXCNwdeQFYqqo5fsTdGYnIVGAb8An/HdvyJIFxX5aPIBKR0QQGDYcSOCF+U1V/LSKDCfS+9AV2Aw+oaq2IRAD/IDBOrwq4X1WP+BN95+VddnxCVRdYLvzhbfe13mw34FVVfVZEYujg+6kuW3wZY4wxxvihq152NMYYY4zxhRVfxhhjjDFBZMWXMcYYY0wQWfFljDHGGBNEVnwZY4wxxgSRFV/GGGOMMUFkxZcxxhhjTBD9B4IGYQclq9xDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fft the signal\n",
    "N = 512                       # fft size\n",
    "X = fft(x, N)\n",
    "mX = np.abs(X)\n",
    "pX = np.angle(X)\n",
    "\n",
    "freq_axis = np.arange(N)/N * fs\n",
    "plt.figure(figsize=(10, 12))\n",
    "ax = plt.subplot(3,1,1)\n",
    "plt.plot(freq_axis, mX)\n",
    "ax.set_title('Magnitude')\n",
    "\n",
    "ax = plt.subplot(3,1,2)\n",
    "plt.plot(freq_axis, pX)\n",
    "ax.set_title('Phase')\n",
    "\n",
    "\n",
    "# ifft it\n",
    "ifft_x = ifft(X)\n",
    "ax = plt.subplot(3,1,3)\n",
    "plt.plot(ifft_x)\n",
    "ax.set_title('Synthesise')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 自己动手写ifft\n",
    "\n",
    "只有两个地方要注意：\n",
    "+ 不要忘记乘上 1/N\n",
    "+ $S_k^*$是$S_k$向量的共轭后的结果。反映在代码中，就是$S_k^*$不要共轭操作之间返回"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hw/anaconda3/lib/python3.7/site-packages/numpy/core/numeric.py:501: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_complex_sinusoid(n, N):\n",
    "    '''\n",
    "    n : time index (or frequency index)\n",
    "    N : number of sample\n",
    "    '''\n",
    "    \n",
    "    k = np.arange(N)\n",
    "    \n",
    "    c_sin = np.exp(1j*2*np.pi*k*n/N)\n",
    "    \n",
    "    return c_sin\n",
    "\n",
    "# ifft loop\n",
    "ifft_x = np.array([])\n",
    "\n",
    "for i in range(N):\n",
    "    s = generate_complex_sinusoid(i, N)\n",
    "    ifft_x = np.append(ifft_x, 1/N * np.sum(X*s))\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(ifft_x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 总结\n",
    "\n",
    "通过自己动手，我们发现IDFT的原来和实现很简单，几乎与DFT一模一样，唯一需要注意的点就是$S_k^*$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
